Category 17: Sishi Regiment

The sishi regiment contains 22 members which are uniform polychora, it also contains several fissaries, exotics, compounds, and scaliforms. Of the 22, sixteen have hyic symmetry, the other six are swirlprisms - of the 16, two have been counted in category 1 as regular, so this category deals with the other 14. Sishi's verf is a dodecahedron, so members of this regiment have verfs which are facetings of the doe, three having uniform verfs. This category also has three noble polychora (has all cells alike as well as all vertices alike). Each polychoron here has hyic symmetry and has 120 vertices. The first 4 are tame, the last 2 as well as the fissary ones are wild, the rest are feral. All of them are orientable. Below are the 14 polychora of this category plus the two fissary ones.

Above are sample slices of the members of this category in the same order as in the text below.

Semiregular

These three have uniform verfs, all of their cells are themselves regular. They have been known since Gosset's time.

764. Sidtixhi - (sid TIK she) small ditrigonary 600-120. Its cells are 120 gikes and 600 tets, its symbol is x(o*oo). Its verf is a sidtid. It has 15840 pieces in four types, LOC = 51.

765. Dittady - (DIT a dee) ditrigonary dis120, its symbol is x(o*'oo^). Its cells are 120 gikes and 120 ikes, it also has pseudo-tets. Its verf is a ditdid. It has 66240 pieces with 8 types, LOC = 153.

766. Gidtixhi - (gid TIK she) great ditrigonary 600-120. Its cells are 600 tet and 120 ikes, it also has pseudo-gikes. Its verf is a gidtid. Its symbol is x(o^o,o). It has 57600 pieces with 8 types, LOC = 154.

Noble Cases

These three have only one type of cell.

767. Idhi - (ID hi) invertidodecahedronary 120. Its cells are 120 ditdids, it also has pseudo-sissids. Its verf is an inverted doe. It has 8640 pieces with two types, LOC = 16.

768. Paphicki - (paf FIK kee) pentagram prismattic 720, also known as small prismosaurus (George Olshevsky). Cells are 720 stips, pseudo cells are pseudo-sissids. Its verf is an inverted doe, it has 8640 pieces of two types and looks like a shallower version of idhi. LOC = 16.

769. Paphacki - (paf FAK kee) pentagon prismattic 720, also known as great prismosaurus (George Olshevsky). Cells are 720 pips, it also has pseudo-gads. Its verf is the dual of H (H is the final stellation of ike). This polychoron is very intricate with a whopping 1,260,000 pieces coming in 90 types - it is by far the most complex in this category with a LOC = 3490.

The Others

These are the remaining eight, each has two types of cells.

770. Ofiddady - (o FID a dee) omnifacetododecahedronary dis120. Its cells are 120 sidtids and 120 ikes, it also has pseudo-sissid+gikes. Its verf is an omnifaceting of doe. It has 66240 pieces in 8 types, LOC = 112.

771. Gridixhi - (grid IK she) great retroinverted dodecahedronary 600-120. Its cells are 120 sidtids and 600 tets, it also has pseudo-sissid+gikes. Its verf is a doe omnifaceting. It has 116,640 pieces with 13 types, LOC = 286.

772. Didhi - (DID hi) dodecahedronary dis120. Its cells are 120 gidtids and 120 gikes, it has pseudo-tets. Its verf is a starrish faceting of doe. It has 19440 pieces with four types, LOC = 61.

773. Sridixhi - (srid IK she) small retroinverted dodecahedronary 600-120. Its cells are 120 gidtids and 600 tets, it also has pseudo-gikes. Its verf is a pseudo-starrish faceting of doe. It has 133,200 pieces with 15 types, LOC = 363.

774. Sridaphi - (srid AH fee) small retroinverted dodecahedronary prismato120. Cells are 120 gikes and 1200 trips, it has pseudo-tets. Verf is a starrish doe faceting. It has 156,240 pieces with 15 types, LOC = 305.

775. Gridaphi - (grid AH fee) great retroinverted dodecahedronary prismato120. Cells are 120 ikes and 1200 trips, it also has pseudo-gikes and pseudo-tets. Its verf is a pseudo-starrish faceting of doe. It has 237,600 pieces with 21 types, LOC = 524.

776. Dophi - (DOFF fee) dodecahedronary prismato120. Its cells are 120 gidtids and 1200 trips, it has pseudo-gikes and pseudo-tets. Its verf is a pseudo-starrish faceting of doe. It has 68400 pieces in eight types, LOC = 137.

777. Radophi - (ra DOFF fee) retrododecahedronary prismato120. Its cells are 120 sidtids and 1200 trips, it also has pseudo-sissid+gikes and pseudo-tets. Its verf is an omnifaceting of doe. It has 66240 pieces in 8 types, LOC = 112.

Fissary

These two are fissary.

F9. Sitpodady - (SIT po da dee) small tripesic dodecahedronary dis120. Its cells are 120 gikes and 120 sidtids. Its verf resembles tiggy a little bit.

F10. Gitpodady - (GIT po da dee) great tripesic dodecahedronary dis120. Its cells are 120 ikes and 120 gidtids. Its verf is a pseudo-starrish faceting of doe.

Conjugates

Below shows how these sishi regiment members pair up as conjugates.

These are self-conjugates: dittady and idhi

These are conjugate pairs: sidtixhi-gidtixhi, paphicki-paphacki, ofiddady-didhi, sridixhi-gridixhi, sridaphi-gridaphi, dophi-radophi, sitpodady-gitpodady.

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