Category 5: Greater truncates


These are the great rhombates, omnitruncates (great prismates), and those with similar vertex figures. These are all lone operatives except for the two fissaries which belong to the sabdiptica regiment from category 17.


Great rhombates

These are the cantitruncated honeycombs and those with related vertex figures. The vertex figures are bilaterally-symmetric tetrahedra. Grich, cuteca, dacta, gaqrich, and caquiteca have chon symmetry while the others have octet symmetry.

92. Grich - Great rhombated cubic honeycomb, also called cantitruncated cubic honeycomb. Cells are gircoes, cubes, and toes. Symbol is o4x3x4x or x3x4x *b3x.

93. Gratoh - Great rhombated tetrahedral-octahedral honeycomb. Cells are gircoes, tics, and tuts. Symbol is x3x4x *b3o.

94. Cuteca - Cubatitruncated cubatiapeiratic honeycomb. Cells are cotcoes, toes, and tosquats. Symbol is o4x3x4/3x4*b or x3x4x4x3*a4/3*c.

95. Dacta - Dicubatitruncated apeiratic honeycomb. Cells are satsas, tics, and quiths. Symbol is o3x4x~x4/3*b.

96. Gaqrich - Great quasirhombated cubic honeycomb. Cells are quitcoes, cubes, and toes. Symbol is o4x3x4/3x or x3x4/3x *b3x.

97. Gaqratoh (also called gaqrahch) - Great quasirhombated tetrahedral-octahedral honeycomb. Cells are quitcoes, quiths, and tuts. Symbol is x3x4/3x *b3o.

98. Caquiteca - Cubatiquasitruncated cubatiapeiratic honeycomb. Cells are cotcoes, toes, and quitsquats. Symbol is o4x3x4x4/3*b or x3x4/3x4/3x3*a4*c.


Omnitruncates

These are the omnitruncates of Wythoffian families. The vertex figures of gippich, quequapech, and dacda are phyllic disphenoids, the rest are irregular tetrahedra. Gippich, quequapech, and dacda have doubled chon symmetry, cadca and dicroch have octet symmetry, and the rest have chon symmetry.

NOTE: In November 2023, Polytope Discord user ThePokemonkey123 discovered that gactipeca and caquitpica are vertex fissary, and in fact belong to the sabdiptica regiment (category 17). Because I exclude fissaries from my main count, this means that numbers 101 and 108 are now unassigned. I'm still trying to figure out whether I should change all later numbers (which would break a lot of citations on the Polytope Wiki), just skip these numbers, or assign them to honeycombs in one of the later categories.

99. Gippich (also called otch) - Great prismated cubic honeycomb, also called omnitruncated cubic honeycomb. Cells are gircoes and ops. Symbol is x4x3x4x.

100. Cutpica - Cubatitruncated prismatocubatiapeiratic honeycomb. Cells are cotcoes, gircoes, tosquats, and stops. Symbol is x4x3x4/3x4*b.

102. Dactapa - Dicubatitruncated prismatoapeiratic honeycomb. Cells are satsas, gircoes, quitcoes, and azips. Symbol is x3x4x~x4/3*b.

103. Cadca - Cubatidicubatiapeiratic honeycomb. Cells are gircoes, quitcoes, toes, and qrasquits. Symbol is x3x3x4x4/3*a.

104. Dicroch - Dicubatirhombated cubatihexagonal honeycomb. Cells are cotcoes, gircoes, quitcoes, and hexats. Symbol is x3x3x4x4/3*a3*c.

105. Dacda - Dicubatidiapeiratic honeycomb. Cells are cotcoes and satsas. Symbol is x4x4/3x4x4/3*a3*c *b~*d.

106. Gaquapech - Great quasiprismated cubic honeycomb. Cells are gircoes, quitcoes, ops, and stops. Symbol is x4x3x4/3x.

107. Quequapech - Quasiquasiprismated cubic honeycomb. Cells are quitcoes and stops. Symbol is x4/3x3x4/3x.

109. Gacquitpica - Great cubatiquasitruncated prismatocubatiapeiratic honeycomb. Cells are cotcoes, quitcoes, quitsquats, and ops. Symbol is x4/3x3x4x4/3*b.

F. Gactipeca - Great cubatitruncated prismatocubatiapeiratic honeycomb. Cells are cotcoes, quitcoes, qrasquits, and stops. Symbol is x4/3x3x4/3x4*b.

F. Caquitpica - Cubatiquasitruncated prismatocubatiapeiratic honeycomb. Cells are cotcoes, gircoes, qrasquits, and ops. Symbol is x4x3x4x4/3*b.


Conjugates

The following honeycombs are self conjugate: dacta, dactapa, cadca, dicroch, dacda, and gaquapech.

The following form conjugate pairs: grich - gaqrich, gratoh - gaqratoh, cuteca - caquiteca, gippich - quequapech, cutpica - gacquitpica, gactipeca - caquitpica.

The following form quasi-conjugate pairs (one set of octagons - octagrams gets swapped, but not the other): gippich - gaquapech, cutpica - gactipeca, cutpica - caquitpica, gactipeca - gacquitpica, caquitpica - gacquitpica, gaquapech - quequapech.


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