These 12 tilings come in four regiments of three. The regiments are srothat, ghothat, sossa, and shaha. Srothat and ghothat form the rhombate and quasirhombate of hexattic symmetry, sossa and shaha are their own special euclidean beasts with apeirogons, sossa is squattic and shaha is hexattic. Rhombated squat is just squat. Each regiment has the first member as the colonel with a trapezoid verf, the second member also wythoffian with a crossed trapezoid verf, and the third member nonwythoffian with a butterfly verf. The butterfly verfed ones can all be made from a blend of omnitruncates, which seems to consistently occur even in dense euclideans. Srothat is convex. The sossa regiment members are the only ones of these that are used in nonprismatic honeycombs.
13: Srothat - Small rhombitrihexagonal tiling. Its faces are triangles, squares, and hexagons. Symbol is x3o6x.
14: Shothat - Small hexatrihexagonal tiling. Its faces are triangles, hexagons, and dodecagons. Symbol is x6x6/5o3*a.
15: Sraht - Small rhombihexagonal tiling. Its faces are squares and dodecagons. Can be formed as a blend of 3 grothats from category 5.
This regiment is mathematically the euclidean analogue to gocco and gaddid. Visually, however, these three don't look very related.
16: Ghothat - Great hexatrihexagonal tiling. Its faces are triangles, hexagons, and dodecagrams. Symbol is x6/5x6o3*a.
17: Qrothat - Quasirhombitrihexagonal tiling. Its faces are triangles, squares, and hexagons. Symbol is x3o6/5x.
18: Graht - Great rhombihexagonal tiling. Its faces are squares and dodecagrams. Can be formed as a blend of 3 quitothits from category 5.
This regiment looks a lot like gocco and gidditdid, and even shares their construction as a convex truncate with stars replacing the big polygons. Do not be fooled though, as far as the coxeter diagrams are concerned these are all entirely unrelated objects. This is the only squattic trapezivert regiment. It has a very impressive superregiment, which we will be seing in more detail in category 8. Everything in this regiment can technically be taken as a kaleidoscopic nonwythoffian with an irregular quadrilateral verf under half symmetry.
19: Sossa - Small squarisquariapeirogonal tiling. Its faces are squares, octagrams, and apeirogons. Symbol is x4/3x4o∞*a. This is our first experience with regiment colonels that have hemifacets. This is not a thing in sphericals, but happens a lot in euclideans.
20: Gossa - Great squarisquariapeirogonal tiling. Its faces are squares, octagons, and apeirogons. Symbol is x4x4/3o∞*a.
21: Sost - Squarisquare tiling. Its faces are octagrams and octagons. Can be formed as a blend of 2 qrasquits or 4 satsas, both from category 5.
Similarly to sossa, this regiment also looks like gocco and gidditdid, but once again is totally unrelated. Sossa and Shaha are more related to eachother than they are to gocco and gidditdid. This regiment also has a very impressive superregiment, which will also be seen in category 8. Everything in this regiment can also technically be taken as a kaleidoscopic nonwythoffian, but there's no subsymmetry. It probably makes a double cover or something.
22: Shaha - Small hexahexaapeirogonal tiling. Its faces are hexagons, dodecagrams, and apeirogons. Symbol is x6/5x6o∞*a.
23: Ghaha - Great hexahexaapeirogonal tiling. Its faces are hexagons, dodecagons, and apeirogons. Symbol is x6x6/5o∞*a.
24: Huht - hexahexagonal tiling. Its faces are dodecagrams and dodecagons. Can be formed as a blend of 3 thotithits or 4 hathas, both from category 5.
Below shows how the trapeziverts pair up as conjugates.
Conjuates:
The following are self-conjugate: sost, huht
The following are conjugate pairs: srothat-qrothat, shothat-ghothat, sraht-graht, sossa-gossa, shaha-ghaha
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