Category 10: Ditetrahedronaries


These are the members of the octet regiment (first listed in category 1) with o3o3o3o3*a (cyclotettic) symmetry. Their vertex figures are tetrahedrally-symmetric facetings of a cuboctahedron. This category mostly corresponds to Bowers' Category 18 polychora.



Primary

263. Datteha - Ditetrahedronary tetrahemiapeiratic honeycomb. Cells are tets and ditathas. Verf is an antitruncated tetrahedron (looks like four tets joined at a point). Symbol is o3o3/2x~o3*b.

264. Dattoha - Ditetrahedronary tetraoctahemiapeiratic honeycomb. Cells are tets, octs, and ditathas.


Secondary

265. Dattetuthah - Ditetrahedronary tetratomotetrahemihexagonal honeycomb. Cells are tets, tuts, and hexats in compounds of three.

266. Dattotuthah - Ditetrahedronary tetraoctatomotetrahemihexagonal honeycomb. Cells are tets, octs, tuts, and hexats.


Coic ones

267. Datetcoha - Ditetrahedronary tetracuboctahemiapeiratic honeycomb. Cells are tets, coes, and ditathas.

268. Datet Tocohaht - Ditetrahedronary tetratomotetracuboctahemihexagonal honeycomb. Cells are tets, tuts, coes, and hexats.


Ohoic ones

269. Dattuthoha - Ditetrahedronary tomotetrahemioctahemiapeiratic honeycomb. Cells are tuts, ohoes, and ditathas.

270. Datetutho - Ditetrahedronary tetratomotetrahemioctahedral honeycomb. Cells are tets, tuts, and ohoes.


Choic ones

271. Radtetutho - Retroditetrahedronary tetratomotetrahemioctahedral honeycomb. Cells are tets, tuts, and choes.

272. Radtatuthoha - Retroditetrahedronary tomotetrahemioctahemiapeiratic honeycomb. Cells are tuts, choes, and ditathas.


Tetracelli-choic ones

273. Datotuthoha - Ditetrahedronary octatomotetrahemioctahemiapeiratic honeycomb. Cells are octs, tuts, choes, and ditathas.

274. Datet Tuthoth - Ditetrahedronary tetratomotetrahemioctahemitriangular honeycomb. Cells are tets, tuts, choes, and trats.

275. Dattotutho - Ditetrahedronary tetraoctatomotetrahemioctahedral honeycomb. Cells are tets, octs, tuts, and choes.


Thah-based ones

These ones have thahs and squats as cells and have no analog in Bowers' category 18, as the edges in the vertex figure corresponding to the hemi-squares are not planar in those categories.

276. Datethahsh - Ditetrahedronary tetrahemihexahemisquare honeycomb. Cells are tets, thahs, and squats. Symbol is (o3o3o4s4/3*a)/2. This is the alternation of cuhsquah from category 1.

277. Datet Hahthash - Ditetrahedronary tetrahemihexahemitriangular hemisquare honeycomb. Cells are tets, thahs, trats, and squats.

278. Dathahasha - Ditetrahedronary hemihexahemisquare hemiapeiratic honeycomb. Cells are thahs, ditathas, and squats.

279. Datet Dituthahash - Ditetrahedronary tetradistomotetrahemihexahemisquare honeycomb. Cells are tets, tuts in two orientations, thahs, and squats.

280. Datdut Thahasha - Ditetrahedronary distomotetrahemihexahemiapeiratihemisquare honeycomb. Cells are tuts in two orientations, thahs, ditathas, and squats.

281. Dattut Hahahash - Ditetrahedronary tomotetrahemihexahemihexagonal hemisquare honeycomb. Cells are tuts, thahs, hexats, and squats.

282. Dattutho Hahash - Ditetrahedronary tomotetrahemioctahemihexahemisquare honeycomb. Cells are tuts, ohoes, thahs, and squats.

283. Datetho Hahahash - Ditetrahedronary tetrahemioctahemihexahemihexagonal hemisquare honeycomb. Cells are tets, ohoes, thahs, hexats, and squats.


Conjugates

The following honeycombs are self conjugate: all.

The following form conjugate pairs: none.


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