Category 3: Rich regiment


Rich is the rectified cubic honeycomb. The rich regiment contains 49 members with four symmetries: chonnic (o4o3x4o), octettic with one edge type (o3x4o *b3o), octettic with two edge types (x3o4o *b3x), and cyclotettic (o3x3o3x3*a). Their vertex figures are facetings of square prisms. There's also a compound of batches. The latter two symmetries were previously put in separate categories called "square podiumverts" and "antifrustumverts" but I decided to merge them into this category.



Rich regiment chonnics

These ones have verfs with full square prism symmetry.

22. Rich - Rectified cubic honeycomb. Cells are octs and coes. Symbol is o4o3x4o, o3x4o *b3o, x3o4o *b3x, or o3x3o3x3*a. Its verf is a square prism. This is also the rectified tetrahedral-octahedral honeycomb.

23. Doha - Disoctahemiapeiratic honeycomb. Cells are octs and thas. Symbol is o4o3x~x3/2*b.

24. Coha - Cuboctahedral hemiapeiratic honeycomb. Cells are coes and thas.

25. Hohah - Hemioctahedral hemiapeiratic honeycomb. Cells are choes and hohas.

26. Ohoha - Octahedral hemioctahedral hemiapeiratic honeycomb. Cells are octs, ohoes, and hohas.

27. Ohohath - Octahedral hemioctahedral hemitrihexagonal honeycomb. Cells are octs, choes, and thats.

28. Hohath - Hemioctahedral hemitrihexagonal honeycomb. Cells are ohoes and thats.


Rich regiment octettics type 1

Under this symmetry rich's verf acts like a rectangular prism.

These six are reverts of fully symmetric honeycombs.

29. Cuhada (also called codaha) - Cubatihemidiapeiratic honeycomb. Cells are coes, thas, and shas. Symbol is (x3o3/2x4/3o4*a~*c)/2.

30. Ocodaha - Octahedral hemioctahedral dihemiapeiratic honeycomb. Cells are octs, coes, thas, and shas.

31. Hahodaha - Hemihexahedral hemioctahedral dihemiapeiratic honeycomb. Cells are thahs, ohoes, shas, and hohas.

32. Hahcohodaha - Hemihexahedral cuboctahedral hemioctahedral dihemiapeiratic honeycomb. Cells are thahs, coes, choes, shas, and hohas.

33. Hahcohohathash - Hemihexahedral cuboctahedral hemioctahedral hemitrihexagonal hemisquare honeycomb. Cells are thahs, coes, ohoes, thats, and squats.

34. Hahohathash - Hemihexahedral hemioctahedral hemitrihexagonal hemisquare honeycomb. Cells are thahs, choes, thats, and squats.

These are the other isotoxal octettic rich regiment members.

35. Hahdhodahthash - Hemihexahedral dihemioctahedral hemitrihexagonal hemisquare honeycomb. Cells are thahs, ohoes, choes, two types of thats, and squats.

36. Ricuhsquah - Rectified cubihemisquare honeycomb. Cells are thahs, coes, and squats. Symbol is (x3o3/2x4o4*a)/2.

37. Retehtrah (also called ridatha) - Rectified tetrahemitriangular honeycomb. Cells are octs, ohoes, and thats. Symbol is x3o3x3o3/2*a3*c.

38. Rohtrah - Rectified octahemitriangular honeycomb. Cells are coes, choes, and thats. Symbol is x3o3x4o4/3*a3*c/2.

39. Hahdha - Hemihexahedral dihemiapeiratic honeycomb. Cells are thahs, thas, and shas.

40. Ohodaha - Octahemioctahedral dihemiapeiratic honeycomb. Cells are ohoes, thas, and hohas.

41. Chodaha - Cubohemioctahedral dihemiapeiratic honeycomb. Cells are choes, shas, and hohas.

42. Hahdcodaha - Hemihexahedral discuboctahedral dihemiapeiratic honeycomb. Cells are thahs, two types of coes, thas, and shas.

43. Ohocodaha - Octahedral hemioctahedral cuboctahedral dihemiapeiratic honeycomb. Cells are octs, coes, ohoes, hohas, and shas.

44. Ocohodaha - Octahedral cuboctahedral hemioctahedral dihemiapeiratic honeycomb. Cells are octs, coes, choes, thas, and hohas.

45. Hahdhohathadha - Hemihexahedral dihemioctahedral hemitrihexagonal dihemiapeiratic honeycomb. Cells are thahs, two types of choes, hohas, shas, and thats.

46. Hahdhohashadha - Hemihexahedral dihemioctahedral hemisquare dihemiapeiratic honeycomb. Cells are thahs, ohoes, choes, hohas, thas, and squats.

47. Hahohohathadha - Hemihexahedral hemioctahedral hemioctahedral hemitrihexagonal dihemiapeiratic honeycomb. Cells are thahs, two types of ohoes, shas, hohas, and thats.

48. Dahohathadha - Dihemioctahedral hemitrihexagonal dihemiapeiratic honeycomb. Cells are ohoes, choes, thats, hohas, and shas.

49. Hahohashadha - Hemihexahedral hemioctahedral hemisquare dihemiapeiratic honeycomb. Cells are thahs, choes, squats, thas, and hohas.

50. Hahohathadha - Hemihexahedral hemioctahedral hemitrihexagonal dihemiapeiratic honeycomb. Cells are thahs, ohoes, thats, thas, and shas.

51. Cohohathadha - Cuboctahedral hemioctahedral hemitrihexagonal hemidiapeiratic honeycomb. Cells are coes, ohoes, thats, thas, and shas.

52. Ohohathadha - Octahedral hemioctahedral hemitrihexagonal hemidiapeiratic honeycomb. Cells are octs, choes, thats, thas, and shas.

53. Hahcohashadha - Hemihexahedral cuboctahedral hemisquare hemidiapeiratic honeycomb. Cells are thahs, coes, two types of thas, and squats.


Rich regiment octettics type 2

Under this symmetry rich's verf acts like a square podium.

54. Hotoh - Hemioctahedral tomooctahedral honeycomb. Cells are choes and toes.

55. Toha - Tomooctahedral hemiapeiratic honeycomb. Cells are toes and hohas.

56. Hotoha - Hemioctahedral tomooctahedral hemiapeiratic honeycomb. Cells are ohoes, toes, and thas.

57. Cotohath - Cuboctahedral tomooctahedral hemitrihexagonal honeycomb. Cells are coes, toes, and thats.

58. Otohath - Octahedral tomooctahedral hemitrihexagonal honeycomb. Cells are two types of octs, toes, and thats.

59. Ohotoh - Octahedral hemioctahedral tomooctahedral honeycomb. Cells are two types of octs, ohoes, and toes.


Rich regiment cyclotettics

Under this symmetry rich's verf acts like a rectangular trapezoprism.

60. Tohohath - Tomooctahedral hemioctahedral hemitrihexagonal honeycomb. Cells are ohoes, toes, and trats.

61. Docohotohath - Disoctahedral cuboctahedral hemioctahedral tomooctahedral hemitrihexagonal honeycomb. Cells are two types of octs, coes, choes, toes, and thats.

62. Dohotoda - Disoctahedral hemioctahedral tomooctahedral disapeiratic honeycomb. Cells are two types of octs, ohoes, toes, thas, and hohas.

63. Cohotoda - Cuboctahedral hemioctahedral tomooctahedral disapeiratic honeycomb. Cells are coes, choes, toes, thas, and hohas.

64. Tohoda - Tomooctahedral hemioctahedral disapeiratic honeycomb. Cells are chos, toes, hohas, and shas.

65. Dahotoda - Dihemioctahedral tomooctahedral disapeiratic honeycomb. Cells are ohoes, choes, toes, thas, and shas.

66. Cotohathadha - Cuboctahedral tomooctahedral hemitrihexagonal dihemiapeiratic honeycomb. Cells are coes, toes, thats, shas, and hohas.

67. Docohotodaha - Disoctahedral cuboctahedral hemioctahedral tomooctahedral dishemiapeiratic honeycomb. Cells are two types of octs, coes, ohoes, toes, hohas, and shas.

68. Docotohathadha - Disoctahedral cuboctahedral tomooctahedral hemitrihexagonal dishemiapeiratic honeycomb. Cells are two types of octs, coes, toes, thats, hohas, and shas.

69. Dodhotodaha - Disoctahedral dishemioctahedral tomooctahedral dishemiapeiratic honeycomb. Cells are two types of octs, ohoes, choes, toes, thas, and shas.

70. Dohotohathadha - Disoctahedral hemioctahedral tomooctahedral hemitrihexagonal dishemiapeiratic honeycomb. Cells are two types of octs, choes, toes, thas, thats, and shas.


Conjugates

The following honeycombs are self conjugate: all.

The following form conjugate pairs: none.


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