figuratenum 0.4.0

A complete generator of infinite sequences of figurate numbers

Figurate Numbers for Python

Plane figurate numbers

1. polygonal_numbers
2. centered_square_numbers = diamond numbers
3. centered_dodecagonal_numbers = star_numbers
4. centered_mgonal_numbers
5. pronic_numbers = heteromecic_numbers = oblong_numbers
6. polite_numbers
7. impolite_numbers
8. cross_numbers
9. aztec_diamond_numbers
10. polygram_numbers(m) = centered_star_polygonal_numbers(m)
11. pentagram_numbers
12. gnomic_numbers
13. truncated_triangular_numbers
14. truncated_square_numbers
15. truncated_pronic_numbers
16. truncated_centered_pol_numbers(m) = truncated_centered_pol_numbers(m)
17. truncated_centered_hexagonal_numbers = truncated_hex_numbers
18. generalized_mgonal_numbers(m, start_numb)
19. generalized_centered_pol_numbers(m, start_numb)
20. generalized_pronic_numbers(start_numb)

Space figurate numbers

1. m_pyramidal_numbers(m)
2. cubic_numbers
3. tetrahedral_numbers
4. octahedral_numbers
5. dodecahedral_numbers
6. icosahedral_numbers
7. truncated_tetrahedral_numbers
8. truncated_cubic_numbers
9. truncated_octahedral_numbers
10. stella_octangula_numbers
11. centered_cube_numbers
12. rhombic_dodecahedral_numbers
13. hauy_rhombic_dodecahedral_numbers
14. centered_tetrahedron_numbers = centered_tetrahedral_numbers
15. centered_square_pyramid_numbers = centered_pyramid_numbers
16. centered_mgonal_pyramid_numbers(m)
17. centered_octahedron_numbers
18. centered_icosahedron_numbers = centered_cuboctahedron_numbers
19. centered_dodecahedron_numbers
20. centered_truncated_tetrahedron_numbers
21. centered_truncated_cube_numbers
22. centered_truncated_octahedron_numbers
23. centered_mgonal_pyramidal_numbers(m)
24. centered_hexagonal_pyramidal_numbers = hex_pyramidal_numbers
25. hexagonal_prism_numbers
26. mgonal_prism_numbers(m)
27. generalized_mgonal_pyramidal_numbers(m, start_num)
28. generalized_cubic_numbers(start_num)
29. generalized_octahedral_numbers(start_num)
30. generalized_icosahedral_numbers(start_num)
31. generalized_dodecahedral_numbers(start_num)
32. generalized_centered_cube_numbers(start_num)
33. generalized_centered_tetrahedron_numbers(start_num)
34. generalized_centered_square_pyramid_numbers(start_num)
35. generalized_rhombic_dodecahedral_numbers(start_num)
36. generalized_centered_mgonal_pyramidal_numbers(m, start_num)
37. generalized_mgonal_prism_numbers(m, start_num)
38. generalized_hexagonal_prism_numbers(start_num)

Multidimensional figurate numbers

1. pentatope_numbers = hypertetrahedral_numbers = triangulotriangular_numbers
2. k_dimensional_hypertetrahedron_numbers(k) = k_hypertetrahedron_numbers(k) = regular_k_polytopic_numbers(k) = figurate_numbers_of_order_k(k)
3. biquadratic_numbers
4. k_dimensional_hypercube_numbers(k) = k_hypercube_numbers(k)
5. hyperoctahedral_numbers = hexadecachoron_numbers = four_cross_polytope_numbers = four_orthoplex_numbers
6. hypericosahedral_numbers = tetraplex_numbers = polytetrahedron_numbers = hexacosichoron_numbers
7. hyperdodecahedral_numbers = hecatonicosachoron_numbers = dodecaplex_numbers = polydodecahedron_numbers
8. polyoctahedral_numbers = icositetrachoron_numbers = octaplex_numbers = hyperdiamond_numbers
9. k_dimensional_hyperoctahedron_numbers(k) = k_cross_polytope_numbers(k)
10. four_dimensional_mgonal_pyramidal_numbers(m) = mgonal_pyramidal_numbers_of_the_second_order
11. k_dimensional_mgonal_pyramidal_numbers(k, m) = mgonal_pyramidal_numbers_of_the_k_2_th_order(k, m)
12. centered_biquadratic_numbers
13. k_dimensional_centered_hypercube_numbers(k)
14. centered_polytope_numbers
15. k_dimensional_centered_hypertetrahedron_numbers(k)
16. centered_hyperoctahedral_numbers = orthoplex_numbers
17. nexus_numbers
18. k_dimensional_centered_hyperoctahedron_numbers(k)