ico_regiment

Category 4 - the Ico Regiment

        Pictured here are the .3 sections of 6 members of the ico regiment, notice the "danglyness" of odho and the strange looking dod honho.  Ihi has ionic icoic symmetry, huhoh and ghahoh has tesseractic symmetry.  Ratho, dod honho, and odho has demitesseractic symmetry.

        The ico regiment consists of 14 polychora (ico is the well known 24-cell).  However only ico has full icoic symmetry, the others have lesser symmetries.  Since ico has already been counted in category 1, this category contains 13 polychora, mentioned below.

62. Ihi (24hemi24) - cells are 24 thahs and 12 coes, has ionic icoic symmetry, verf has pyrito symmetry.

63. Ratho (rectified tesseractihemioctachoron (tho)) - cells are 8 thahs, 8 octs, and 4 coes, has demitesseractic (DT) symmetry.  Verf is a square bowtie prism.

64. Oh (octahemi16) - cells are 8 octs and 8 ohoes - has tesseractic symmetry.  Verf is a square inflectoprism (looks like 2 square pyramids dangling off each other).

65. Shahoh (small 16hemi16) - cells are 16 octs and 8 ohoes - has tesseractic symmetry.  Verf is an inverted square prism.

66. Odho (8dishemi8) - cells are 8 thahs, 4 ohoes, and 4 choes - has DT symmetry.  Verf is a square bowtie inflectoprism.

67. Huhoh (16hemi16) - cells are 16 thahs and 8 choes - has tesseractic symmetry.  Verf  has 4 square bowties connected in a ring with the long edges connecting to the 4 long bowties going through the center.

68. Hohoh (16-8hemi16) - cells are 8 octs, 16 thahs, and 8 choes - has tesseractic symmetry, verf looks like cube with huhoh verf removed.

69. Ohuhoh (8-16 hemi16 - cells are 8 octs, 16 thahs, and 8 coes - has tesseractic symmetry, verf looks like huhoh verf fused with oh verf.

70. Ghahoh (great 16hemi16) - cells are 16 thahs and 8 coes - has tesseractic symmetry, verf looks like cube with ohuhoh verf removed.

71. Hodho (16-8dishemi8) - cells are 16 octs, 8 thahs, 4 choes, and 4 ohoes - has DT symmetry, verf looks like cube with odho verf removed.

72. Hoh Honho (16-8hemi16intercepted hemi8) - cells are 24 thahs (acting like 8+16, not like icoic), 8 choes, and 4 coes.  Has DT symmetry, verf looks like ohuhoh verf with odho verf removed in such a way that 6 square bowties are on the surface.

73. Dod Honho (dis8dishemi8intercepted hemi8) - cells are 16 thahs, 4 coes, 4 choes, and 4 ohoes, has DT symmetry, verf looks like bowtie prism with odho verf removed in such a way that the squares of the bowtie prism turn to bowties.

74. Doh Honho (dis8hemi16intercepted hemi8) - cells are 8 thahs, 8 octs, 8 ohoes, and 4 coes, has DT symmetry, verf looks like shahoh's with an odho verf removed.

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