Category S1: Simple Scaliforms

These are the more simpler scaliforms, six have prismatic symmetries and three belong (or almost belongs) to the hex regiment. Two new ones have been found in 2020.

Prismatic Cases

Verfs of the Prismatic Scaliforms

These have prismatic symmetries.

Tutcup - (TUT cup / truncated tetrahedral cupoliprism) - cells are 2 tuts, 6 tets, and 8 tricus. This object is convex with 24 vertices. Tuts are trans-arranged, tets are perpendicular to tuts, connecting to them by edge, tricus (tricu = trigonal cupola) connect to tuts by their base faces, and connect to each other by the squares. Tets and tricus connect by triangles. Verf is a rectangle skew pyramid. Tutcup was discovered by Richard Klitzing while he was investigating segmentachora. Every dimension beyond four also has a tutcup-like polytope. It is tame and orientable.

Hossdap - (HOSS dap / hollow small stellated dodecahedral antiprism) - cells are 12 staps (5/2 AP) and 24 stappies (star pyramid). Hossdap has 24 vertices arranged similar to the sissid prism. It also has 2 binary pseudo-sissids as caps, which looks like sissid shaped hollows that form a hole that burrows through the center. All connections are of the variety stap-stappy, they can either connect by star or triangle. Verf is a "stiscu" (star semicupola) which is a star atop hollow pentagon trans-arranged. I discovered hossdap not long after tutcup was found. It is tame and non-orientable.

Siidcup - (SIDE cup / small icosicosidodecahedral cupoliprism) - cells are 2 siids, 12 staps, and 40 tricus. This one has 120 vertices arranged similar to the siid prism. Stars connect siids to staps, tricus connect to siids by it's cap faces. Triangles connect staps to tricus, while tricus connect to each other by squares. Verf is a skewed wedge. I found this one in summer 2005. It is tame and orientable.

Dastop - (DASS tup / dodecastar toroidiprism) - cells are 12 staps and 24 stiscus. Dastop has 60 vertices arranged like a shortened did prism. Stars and triangles connect staps to stiscus, while stiscus connect to each other by squares. The stars are arranged sort of like the stars in the did prism (diddip), so the caps are actually 2 "12 stars of did"s. This object has chasms. Verf is a sort of butterfly skew prism. I found this one on October 22, 2005. It is tame and non-orientable.

Hog Dhidicup - (hog THID ih kup / hollow great dodecahemidodecahedral cupoliprism) - cells are 12 staps and 24 rastacus. Hog dhidicup has the vertices of a stretched id prism. Verf is a faceting of a polyhedron similar to affixthi's verf. It was discovered by _Geometer in 2020.

Hocucup - (HO ku kup / hollow cuboid cupoliprism) - cells are 12 tets as 6 soes and 12 two-trip blends. It has the vertices of cope. Its verf is a butterfly wedge. It was discovered by _Geometer in 2020.

Hex Scaliforms

Verfs of the Hex Scaliforms

These polychora are in the hex regiment. Each with 8 vertices.

Koho - (KO ho / skew-octahemioctachoron) - cells are 8 tets and 4 bobipyrs (bowtie-bipyramid). The tets are arranged in a skewed octagon arrangement, to help see this, take a tesseract and chose 8 vertices in the following pattern: Start with a vertex, and trace along in the following directions, x, y, z, w, -x, -y, -z, -w. Then find the tets of hex which correspond to those vertices, and fill in the blanks with bobipyrs. Verf looks like a right triangle bipyramid with the two halves twisted off kilter, so that a bowtie face will show at the equator. Andrew Weimholt found this one in February 2006 after I described the two new uniform polytera (phap and nophap) in the tac regiment to him. It is wild and orientable.

Hatho - (HATH tho / hemi-tesseractihemioctachoron) - cells are 4 tets and 4 bobipyrs. This polychoron can be found by taking a tho, and chopping off two quadrants (upper-north, and lower-south for instance). The verf is a bowtie pyramid. I found this one in February 2006 when trying to decipher Andrew Weimholt's koho. It is tame and orientable. It doesn't have all of the edges of hex, so it is "almost in" the hex regiment.

Setho - (SETH tho / sesqui-tesseractihemioctachoron) - cells are 12 tets and 4 bobipyrs. This polychoron is the blend of hex and hatho. Its verf is an oct with two octants missing. I found this one in February 2006 after I found hatho. It is wild and non-orientable.


Below shows how the simple scaliforms pair up as conjugates.


The following are self conjugates: tutcup, koho, hatho, setho.

The following have no uniform conjugates: hossdap, siidcup, dastop.

Category 29: Dircospids --- back to Polychoron Page --- Category S2: Podary Scaliforms