Module: FigurateNumbers::SpaceFigurateNumbers

Extended by:
SpaceFigurateNumbers
Included in:
FigurateNumbers, SpaceFigurateNumbers
Defined in:
lib/figurate_numbers/space_figurate_numbers.rb

Overview

Module containing methods for generating 3D figurate number sequences.

Instance Method Summary collapse

Instance Method Details

#centered_cube ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 352

def centered_cube
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (delta**2 - delta + 1)
    end
  end
end

#centered_decagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 555

def centered_decagonal_pyramidal
  m = 10
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m * delta**3 + delta * (6 - m)) / 6
    end
  end
end

#centered_dodecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 573

def centered_dodecagonal_pyramidal
  m = 12
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m * delta**3 + delta * (6 - m)) / 6
    end
  end
end

#centered_dodecahedron ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 454

def centered_dodecahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (3 * delta**2 - 3 * delta + 1)
    end
  end
end

#centered_hendecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 564

def centered_hendecagonal_pyramidal
  m = 11
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m * delta**3 + delta * (6 - m)) / 6
    end
  end
end

#centered_heptagonal_pyramid ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 420

def centered_heptagonal_pyramid
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (delta**2 - delta + 1)
    end
  end
end

#centered_heptagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 528

def centered_heptagonal_pyramidal
  m = 7
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m * delta**3 + delta * (6 - m)) / 6
    end
  end
end

#centered_hexagonal_pyramid ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 412

def centered_hexagonal_pyramid
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (5 * delta**2 - 5 * delta + 6) / 6
    end
  end
end

#centered_hexagonal_pyramidal ⇒ Object Also known as: hex_pyramidal 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 518

def centered_hexagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**3
    end
  end
end

#centered_icosahedron ⇒ Object Also known as: centered_cuboctahedron 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 444

def centered_icosahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (5 * delta**2 - 5 * delta + 3) / 3
    end
  end
end

#centered_mgonal_pyramid(m) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 396

def centered_mgonal_pyramid(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m - 1) * ((delta - 1) * delta * (2 * delta - 1)) / 6 + (2 * delta - 1)
    end
  end
end

#centered_mgonal_pyramidal(m) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 486

def centered_mgonal_pyramidal(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m * delta**3 + delta * (6 - m)) / 6
    end
  end
end

#centered_nonagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 546

def centered_nonagonal_pyramidal
  m = 9
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m * delta**3 + delta * (6 - m)) / 6
    end
  end
end

#centered_octagonal_pyramid ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 428

def centered_octagonal_pyramid
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (7 * delta**2 - 7 * delta + 6) / 6
    end
  end
end

#centered_octagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 537

def centered_octagonal_pyramidal
  m = 8
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (m * delta**3 + delta * (6 - m)) / 6
    end
  end
end

#centered_octahedron ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 436

def centered_octahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (2 * delta**2 - 2 * delta + 3) / 3
    end
  end
end

#centered_pentagonal_pyramid ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 404

def centered_pentagonal_pyramid
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (2 * delta**2 - 2 * delta + 3) / 3
    end
  end
end

#centered_pentagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 510

def centered_pentagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (5 * delta**3 + delta) / 6
    end
  end
end

#centered_square_pyramid ⇒ Object Also known as: centered_pyramid 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 386

def centered_square_pyramid
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * ((delta**2 - delta + 2)) / 2
    end
  end
end

#centered_square_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 502

def centered_square_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta**3 + delta) / 3
    end
  end
end

#centered_tetrahedron ⇒ Object Also known as: centered_tetrahedral 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 376

def centered_tetrahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * ((delta**2 - delta + 3)) / 3
    end
  end
end

#centered_triangular_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 494

def centered_triangular_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta**2 + 1) / 2
    end
  end
end

#centered_truncated_cube ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 470

def centered_truncated_cube
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (23 * delta**2 - 23 * delta + 3) / 3
    end
  end
end

#centered_truncated_octahedron ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 478

def centered_truncated_octahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (5 * delta**2 - 5 * delta + 1)
    end
  end
end

#centered_truncated_tetrahedron ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 462

def centered_truncated_tetrahedron
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (7 * delta**2 - 7 * delta + 3) / 3
    end
  end
end

#cubic ⇒ Object Also known as: perfect_cube 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 276

def cubic
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**3
    end
  end
end

#decagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 64

def decagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (8 * delta - 5) / 6
    end
  end
end

#dodecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 80

def dodecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (10 * delta - 7) / 6
    end
  end
end

#dodecahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 304

def dodecahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (3 * delta - 1) * (3 * delta - 2)) / 2
    end
  end
end

#generalized_centered_cube(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 656

def generalized_centered_cube(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (delta**2 - delta + 1)
    end
  end
end

#generalized_centered_mgonal_pyramidal(m, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 688

def generalized_centered_mgonal_pyramidal(m, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y <<  (m * delta**3 + delta * (6 - m)) / 6
    end
  end
end

#generalized_centered_square_pyramid(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 672

def generalized_centered_square_pyramid(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y <<  ((2 * delta - 1) * (delta**2 - delta + 2)) / 2
    end
  end
end

#generalized_centered_tetrahedron(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 664

def generalized_centered_tetrahedron(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y <<  (2 * delta - 1) * (delta**2 - delta + 3) / 3
    end
  end
end

#generalized_cubic(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 624

def generalized_cubic(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta**3
    end
  end
end

#generalized_dodecahedral(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 648

def generalized_dodecahedral(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (9 * delta**2 - 9 * delta + 2) * delta /  2
    end
  end
end

#generalized_hexagonal_prism(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 704

def generalized_hexagonal_prism(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta * (3 * delta**2 - 3 * delta + 1)
    end
  end
end

#generalized_hexagonal_pyramidal(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 615

def generalized_hexagonal_pyramidal(left_index = 0)
  m = 6
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * ((m - 2) * delta - m + 5)) / 6
    end
  end
end

#generalized_icosahedral(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 640

def generalized_icosahedral(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (5 * delta**2 - 5 * delta + 2) * delta / 2
    end
  end
end

#generalized_mgonal_prism(m, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 696

def generalized_mgonal_prism(m, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << delta * (m * delta**2 - m * delta + 2) / 2
    end
  end
end

#generalized_mgonal_pyramidal(m, left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 598

def generalized_mgonal_pyramidal(m, left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * ((m - 2) * delta - m + 5)) / 6
    end
  end
end

#generalized_octahedral(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 632

def generalized_octahedral(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (2 * delta**2 + 1) * delta / 3
    end
  end
end

#generalized_pentagonal_pyramidal(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 606

def generalized_pentagonal_pyramidal(left_index = 0)
  m = 5
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * ((m - 2) * delta - m + 5)) / 6
    end
  end
end

#generalized_rhombic_dodecahedral(left_index = 0) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 680

def generalized_rhombic_dodecahedral(left_index = 0)
  Enumerator.new do |y|
    ((-1 * left_index.abs)..Float::INFINITY).each do |delta|
      y <<  delta**4 - (delta - 1)**4
    end
  end
end

#hauy_rhombic_dodecahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 368

def hauy_rhombic_dodecahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (8 * delta**2 - 14 * delta + 7)
    end
  end
end

#hendecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 72

def hendecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (9 * delta - 6) / 6
    end
  end
end

#heptadecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 120

def heptadecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (15 * delta - 12) / 6
    end
  end
end

#heptagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 40

def heptagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (5 * delta - 2) / 6
    end
  end
end

#hexadecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 112

def hexadecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (14 * delta - 11) / 6
    end
  end
end

#hexagonal_prism ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 582

def hexagonal_prism
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (3 * delta**2 - 3 * delta + 1)
    end
  end
end

#hexagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 32

def hexagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (4 * delta - 1) / 6
    end
  end
end

#icosagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 144

def icosagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (18 * delta - 15) / 6
    end
  end
end

#icosahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 312

def icosahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (5 * delta**2 - 5 * delta + 2)) / 2
    end
  end
end

#icosidigonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 160

def icosidigonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (20 * delta - 17) / 6
    end
  end
end

#icosihenagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 152

def icosihenagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (19 * delta - 16) / 6
    end
  end
end

#icosiheptagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 200

def icosiheptagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (25 * delta - 22) / 6
    end
  end
end

#icosihexagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 192

def icosihexagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (24 * delta - 21) / 6
    end
  end
end

#icosinonagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 216

def icosinonagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (27 * delta - 24) / 6
    end
  end
end

#icosioctagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 208

def icosioctagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (26 * delta - 23) / 6
    end
  end
end

#icosipentagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 184

def icosipentagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (23 * delta - 20) / 6
    end
  end
end

#icositetragonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 176

def icositetragonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (22 * delta - 19) / 6
    end
  end
end

#icositrigonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 168

def icositrigonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (21 * delta - 18) / 6
    end
  end
end

#mgonal_prism(m) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 590

def mgonal_prism(m)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (m * delta**2 - m * delta + 2) / 2
    end
  end
end

#nonadecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 136

def nonadecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (17 * delta - 14) / 6
    end
  end
end

#nonagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 56

def nonagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (7 * delta - 4) / 6
    end
  end
end

#octadecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 128

def octadecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (16 * delta - 13) / 6
    end
  end
end

#octagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 48

def octagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (6 * delta - 3) / 6
    end
  end
end

#octahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 296

def octahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (2 * delta**2 + 1)) / 3
    end
  end
end

#pentadecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 104

def pentadecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (13 * delta - 10) / 6
    end
  end
end

#pentagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 24

def pentagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta**2 * (delta + 1) / 2
    end
  end
end

#r_pyramidal(r = 3) ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 6

def r_pyramidal(r = 3)
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (3 * delta**2 + delta**3 * (r - 2) - delta * (r - 5)) / 6
    end
  end
end

#rhombic_dodecahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 360

def rhombic_dodecahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (2 * delta - 1) * (2 * delta**2 - 2 * delta + 1)
    end
  end
end

#square_pyramidal ⇒ Object Also known as: pyramidal 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 14

def square_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (2 * delta + 1)) / 6
    end
  end
end

#square_square_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 259

def square_square_pyramidal
  Enumerator.new do |y|
    finite_set = [1, 4900]
    (0..Float::INFINITY).each do |delta|
      y << finite_set[delta % 2]
    end
  end
end

#square_tetrahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 250

def square_tetrahedral
  Enumerator.new do |y|
    finite_set = [1, 4, 19_600]
    (0..Float::INFINITY).each do |delta|
      y << finite_set[delta % 3]
    end
  end
end

#stella_octangula ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 344

def stella_octangula
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (2 * delta**2 - 1)
    end
  end
end

#tetradecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 96

def tetradecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (12 * delta - 9) / 6
    end
  end
end

#tetrahedral ⇒ Object Also known as: triangular_pyramidal 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 286

def tetrahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (delta * (delta + 1) * (delta + 2)) / 6
    end
  end
end

#tetrahedral_square_pyramidal_number ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 268

def tetrahedral_square_pyramidal_number
  Enumerator.new do |y|
    (1..Float::INFINITY).each do
      y << 1
    end
  end
end

#triacontagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 224

def triacontagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (28 * delta - 25) / 6
    end
  end
end

#triangular_square_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 241

def triangular_square_pyramidal
  Enumerator.new do |y|
    finite_set = [1, 55, 91, 208_335]
    (0..Float::INFINITY).each do |delta|
      y << finite_set[delta % 4]
    end
  end
end

#triangular_tetrahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 232

def triangular_tetrahedral
  Enumerator.new do |y|
    finite_set = [1, 10, 120, 1540, 7140]
    (0..Float::INFINITY).each do |delta|
      y << finite_set[delta % 5]
    end
  end
end

#tridecagonal_pyramidal ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 88

def tridecagonal_pyramidal
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << delta * (delta + 1) * (11 * delta - 8) / 6
    end
  end
end

#truncated_cubic ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 328

def truncated_cubic
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (3 * delta - 2)**3 - ((8 * (delta - 1) * delta * (delta + 1)) / 6)
    end
  end
end

#truncated_octahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 336

def truncated_octahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (16 * delta**3 - 33 * delta**2 + 24 * delta - 6)
    end
  end
end

#truncated_tetrahedral ⇒ Object 



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# File 'lib/figurate_numbers/space_figurate_numbers.rb', line 320

def truncated_tetrahedral
  Enumerator.new do |y|
    (1..Float::INFINITY).each do |delta|
      y << (23 * delta**2 - 27 * delta + 10) * delta / 6
    end
  end
end