Category 7: Bitruncates

deca tah cont xhi shihi dahi gixhi gic ghihi


There are 9 bitrucates plus an two additional fissary cases. Of the bitruncates, 4 are convex, 3 are starry and 2 are biquasitruncates. They all have disphenoid verfs. Below are the 9 bitruncates plus the 2 fissary cases.
Bitruncates

Convex Bitruncates

Verfs of the Convex Bitruncates

These four are convex, two of them, deca and cont, are noble (all cells alike as well as all vertices alike).

298. Deca - (DECK uh) decachoron. Its symbol is oxxo, it has 30 verts. Its cells are 10 tuts. It has 10 pieces of one type and has deca (double pennic) symmetry. It is convex and noble. LOC = 3.

299. Tah - (TA) tesseracti16. Its symbol is oxx'o (also o$x), it has 96 verts. Its cells are 8 toes and 16 tuts. It has 24 pieces of two types and has tessic symmetry. LOC = 6.

300. Cont - (CONT) tetracontoctachoron (also called 48-cell or octagonny (Wendy Kreiger)). It's symbol is ox'xo, and it has 288 verts. It has 48 tics and therefore 48 pieces of one type. It has contic symmetry (double icoic). It is convex and noble, LOC = 3.

301. Xhi - (ZHI) 600-120. Its symbol is oxx^o and has 3600 verts. Its cells are 120 tis and 600 tuts. It has 720 pieces of two types and is hyic, LOC = 6.


Starry Bitruncates

Verfs of the Starry Bitruncates

These three are the starry ones. All of these have hyic symmetry and 3600 vertices.

302. Shihi - (SHI hi) small 120-120. Its symbol is ox^x*o. It has 120 tigids and 120 tids. It has 2520 pieces with two types, LOC = 17.

303. Dahi - (DAY hi) dis120. Its symbol is o*xx^o. The cells are 120 tiggies and 120 tis. It has 21720 pieces with four types, LOC = 75.

304. Gixhi - (GIK she) great 600-120. Its symbol is oxx*o. Its cells are 120 tiggies and 600 tuts. It has 122,640 pieces of 14 types, LOC = 494. Gixhi is the complex winner of this category.


Biquasitruncates

Verfs of the Biquasitruncates

There are two of these, gic and ghihi - where gic is noble.

305. Gic - (GIC) great 48 (also called octagrammy by Wendy Kreiger). Its symbol is ox"xo, and it has 288 verts. Its cells are 48 quiths. It is a noble uniform polychoron with 3840 pieces of three types. LOC = 60.

306. Ghihi - (GI hi) great 120-120. Its symbol is ox^'x^o, and it has 3600 verts. Its cells are 120 quit sissids and 120 quit gissids. It is quite wild looking with 68640 pieces in nine types, LOC = 254.


Fissary Cases

Verfs of the Fissary Bitruncates

These two are fissary, both have 600 vertices (acts like 1800 that triples up) and have hyic symmetry. These two could belong to category 18, since they are inside those regiments. Both of them are also noble fissaries. Piece counts and LOCs have yet to be calculated.

F1. Sitphi - (SIT fee) small tripesic 120. Its symbol is o*x^x*o. Its cells are 120 tigids. Its verf is a compound of three long disphenoids. It belongs to the sidtaxhi regiment.

F2. Gitphi - (GIT fee) great tripesic 120. Its symbol is o^x*'x^o. Its cells are 120 quit sissids. Its verf is a compound of 3 flat disphenoids. It belongs to the gadtaxady regiment.

There's also a similar object in the dattady regiment, but it is a compound.

Conjugates

Below shows how the bitruncates pair up as conjugates.

Conjugates

The following are self conjugates: deca, tah, and dahi.

The following are conjugate pairs: cont-gic, xhi-gixhi, shihi-ghihi, and sitphi-gitphi.

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