Category 4: Rat Regiment


HOOOWEEE - this place is full of rats! - well actually the regiment of polytera based off of the rectified pentacross (Rat, short for rectified triacontaditeron). Rat could be considered as the 5-D version of ico, its symbol is oxoo'o and its verf is an octahedral prism. Rat has 40 vertices and 240 edges. The rat regiment contains 44 members plus a compound. We could split this regiment into five groups - the main full symmetrics, the full symmetric pairs, the rhohid group, and the main demi symmetrics, and the demi symmetric pairs - plus a sixth group - the lone compound named bic.
Hanoh

Main Full Symmetrics

Verfs of the Main Full Symmetrics of Rat Regiment

There are seven main members with full penteract symmetry, their verfs are above. The tame ones are rat, thit, rithit, and rinhit - others are wild. Rat and rithit are orientable, the others are not.

48. Rat - (RAT) rectified triacontaditeron, or rectified pentacross. The symbol is oxoo'o = ox8o. It has 10 hexes and 32 raps. Its verf is an ope. It is the kissing polytope of 5-D, so go out and kiss a rat :P.

49. Thit - (THIT) 32hemi32teron. It has 32 raps and 16 duhds. It is the 5-D version of shahoh.

50. Rithit - (RITH it) retro32hemi32teron. It has 32 firps and 16 spids.

51. Onthet - (ON thet) octary penteracti32hemi32teron. It has 32 firps, 10 hexes, and 16 phuds.

52. Otnahit - (OT na hit) octary 32penteractihemi32teron. It has 32 pinnips, 10 hexes, and 16 spids.

53. Ithit - (ITH it) inverti32hemi32teron. It has 32 pinnips and 16 phuds.

54. Rinhit - (RIN hit) retropenteractihemi32teron. It has 10 hexes and 16 duhds. This is the 5-D version of oh.

Below are fields of sections of the main full symmetrics of the rat regiment.

Sections of the Main Full Symmetrics of Rat Regiment


Full Symmetric Pairs

Verfs of the Full Symmetric Pairs of Rat Regiment

There are six pairs of rat members with full penteract symmetry, twelve polytera in all, their verfs are above. Each pair has one member with opes (the ones with a c in the name) and one with tisdips (has a b). The tame ones are rat, thit, rithit, and rinhit - others are wild. Rat and rithit are orientable, the others are not.

55. Cathit - (CATH it) celli32hemi32teron. It has 32 raps, 16 spids, and 40 opes.

56. Bathit - (BATH it) biprismato32hemi32. It has 32 raps, 16 spids, and 80 tisdips.

57. Cant - (CANT) cellipenteracti32teron. It has 10 hexes, 32 firps, and 40 opes.

58. Bant - (BANT) biprismatopenteracti32teron. It has 10 hexes, 32 firps, and 80 tisdips.

59. Ratchet - (RATCH it) retro32cellihemi32teron. It has 32 firps, 16 duhds, and 40 opes. Come to think of it, some of the 3-D cross sections of this polytope looks like it would fit in the game Ratchet and Clank.

60. Ratobaht - (ra TO bot) retro32biprismatohemi32teron. It has 32 firps, 16 duhds, and 80 tisdips. I so wanted to call this one "Clank".

61. Cat - (CAT) celli32teron. It has 32 pinnips and 40 opes. Uh oh, there's a cat loose amongst the rats.

62. Bat - (BAT) biprismato32teron. It has 32 pinnips and 80 tisdips.

63. Conhit - (CON hit) cellipenteractihemi32teron. It has 10 hexes, 16 spids, and 40 opes.

64. Bonhit - (BON hit) biprismatopenteractihemi32teron. It has 10 hexes, 16 spids, and 80 tisdips.

65. Chet - (CHET) cellihemi32teron. It has 16 phuds and 40 opes.

66. Boht - (BOAT) biprismatohemi32teron. It has 16 phuds and 80 tisdips.

Below are fields of sections of the full symmetric pairs of the rat regiment.

Sections of the Full Symmetric Pairs of Rat Regiment


Rhohid Group

Verfs of the Rhohid Group

Rhohid is the rectified hehad, the 5-D version of ratho. These thirteen members which includes rhohid, have thos and icoes as facets. All of these are non-orientable and only rhohid is tame, the others are wild. These have demipenteract (hinnic) symmetry. Verfs are above in sections.

67. Rhohid - (RO hid) rectified 16hemidecateron. It has 10 thoes, 5 icoes, and 16 raps.

68. Bendhehad - (BEN the had) biprismatopenteractidis16hemidecateron. It has 10 thoes, 5 icoes, 16 firps, 16 pinnips, and 80 tisdips.

69. Nabadhehad - (na BA the had) penteractibiprismatodis16hemidecateron. It has 10 thoes, 5 icoes, 16 raps, 16 spids, and 80 tisdips.

70. Nathehid - (NATH e hid) penteractitris16hemidecateron. It has 10 thoes, 5 icoes, 16 firps, 16 pinnips, and 16 spids.

71. Nedhehad - (NED e had) penteractidis16hemidecateron. It has 10 thoes, 5 icoes, 16 raps, and 16 duhds.

72. Benthahid - (BEN tha hid) biprismatopenteractitris16hemidecateron. It has 10 thoes, 5 icoes, 16 firps, 16 pinnips, 16 duhds, and 80 tisdips.

73. Thinhed - (THIN hed) tris16penteractihemidecateron. It has 10 thoes, 5 icoes, 16 firps, 16 pinnips, and 16 phuds.

74. Hinhohid - (hin HO hid) 16penteracti16hemidecateron. It has 10 thoes, 5 icoes, 16 pinnips, and 16 piphids.

75. Dohbinhed - (DOE bin hed) dis16biprismatopenteractihemidecateron. It has 10 thoes, 5 icoes, 16 pinnips, 16 piphids, and 80 tisdips.

76. Nabthehid - (NAB the hid) penteractibiprismatotris16hemidecateron. It has 10 thoes, 5 icoes, 16 raps, 16 firps, 16 piphids, and 80 tisdips.

77. Didhehad - (DID he had) decadis16hemidecateron. It has 10 thoes, 5 icoes, 16 pinnips, and 16 nipdips.

78. Nadahobhid - (nod THA vid) penteractidis16biprismatohemidecateron. It has 10 thoes, 5 icoes, 16 pinnips, 16 nipdips, and 80 tisdips.

79. Dathehid - (DATH e hid) decatris16hemidecateron. It has 10 thoes, 5 icoes, 16 raps, 16 firps, and 16 nipdips.

Below are fields of sections of the rhohid group of the rat regiment.

Sections of the Rhohid Group of Rat Regiment


Main Demi Symmetrics

Verfs of the Main Demi Symmetrics

These four have hinnic symmetry but they have no icoes or thoes. They are all non-orientable. Hah is tame, the others are wild. Verfs are above in sections.

80. Hah - (HAH) hexadecahexadecateron. It has 16 firps and 16 piphids.

81. Noth - (NOTH) penteractitris16teron. It has 10 hexes, 16 raps, 16 pinnips, and 16 piphids.

82. Hanoh - (HAY no) 16penteracti16teron. It has 10 hexes, 16 firps, and 16 nipdips.

83. Tuh - (TUH) trishexadecateron. It has 16 raps, 16 pinnips, and 16 nipdips.

Below are fields of sections of the main demi symmetrics of the rat regiment.

Sections of the Main Demi Symmetrics of Rat Regiment


Demi Symmetric Pairs.

Verfs of the Demi Symmetric Pairs

These eight come in four pairs. Like the other paired ones, each pair has a member with opes and one with tisdips. All of these are non-orientable and wild. The verfs are above.

84. Candoh - (CAN doe) cellipenteractidis16teron. It has 10 hexes, 16 firps, 16 piphids, and 40 opes.

85. Bandoh - (BAN doe) biprismatopenteractidis16teron. It has 10 hexes, 16 firps, 16 piphids, and 80 tisdips.

86. Cath - (CATH) cellitris16teron. It has 16 raps, 16 pinnips, 16 piphids, and 40 opes.

87. Bath - (BATH) biprismatotris16teron. It has 16 raps, 16 pinnips, 16 piphids, and 80 tisdips.

88. Cadoh - (KAY doe) cellidis16teron. It has 16 firps, 16 nipdips, and 40 opes.

89. Badoh - (BAY doe) biprismatodis16teron. It has 16 firps, 16 nipdips, and 80 tisdips.

90. Canth - (CANTH) cellipenteractitris16teron. It has 10 hexes, 16 raps, 16 pinnips, 16 nipdips, and 40 opes.

91. Banth - (BANTH) biprismatopenteractitris16teron. It has 10 hexes, 16 raps, 16 pinnips, 16 nipdips, and 80 tisdips.

Below are fields of sections of the demi symmetric pairs of the rat regiment.

Sections of the Demi Symmetric Pairs of Rat Regiment


Lone Compound.

Verf of Bic

The only pure compound here is bic, which is the compound of 10 squocts. It is tame and orientable. Verf is above.

C. Bic - (BIK) biprismatocelliteron. It has 40 opes and 80 tisdips. This could be considered as the 5-D version of gico.

Below are fields of sections of bic.

Sections of Bic


Below are poke sections of each of the rat regiment members in same order as the list, includes bic at the end. Take note, that these polyhedral shapes are nothing more than 3-D "needle pricks" of the 5 dimensional objects.

Rat Fusion


Conjugates

Below shows how the rectates pair up as conjugates.

Conjugates

The following are self conjugates: all.

The following are conjugate pairs: none.

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