Category 19: Miscellaneous

The miscellaneous category belongs to small groups of atypical polytera, so far there are 7 known atypical polytera that doesn't belong in categories A-D. Two were counted already - phap and nophap from category 1. The other 5 are here and they come in two types. The first type are the Johnson antiprisms of five dimensions and the other three form a newly discovered regiment - hosiap, which is the blend of 6 hins (demipenteracts). Any undiscovered atypicals will go in this category as long as they form small groupings. Any large groups will form new categories, wonder if there are any out there.

Johnson Antiprisms

Johnson Antiprism Verfs

These two were found by Norman Johnson several decades ago, they are antiprism like figures with bases based off of two polychora from category 18. These have "hipe" symmetry (120-cell prism symmetry) and they each have 1200 vertices and are lone members in their regiments. Both are tame and orientable. Above are the verfs as a series of cross sections.

1288. Sidtaxhiap - (sid TAK she yap) small ditetrahedrary 600-120choron antiprism. Its symbol is ooo^s s. It has 2 sidtaxhis, 120 sidtidaps, and 1200 pens.

1289. Gadtaxhiap - (gad TAK she yap) grand ditetrahedrary 600-120choron antiprism. Its symbol is ooo*'s s. It has 2 gadtaxhis, 120 gidtidaps, and 1200 pens.

Hosiap Regiment

Hosiap Regiment Verfs

The hosiap regiment is formed by blending 6 demipenteracts together. The members either have icope (ico prism) symmetry or chiro-icope symmetry. The verf of hosiap is a blend of two raps. These have 48 vertices. There are three uniform members, 5 scaliforms, and 6 uniform chiral compounds (contains 3 of the same hin member). The compounds aren't true regiment members sense they lack some of the edges. Above are the verfs as a series of cross sections.

1290. Hosiap - (HOSS e yap) hollostellicosatetrachoron antiprism. It has 48 hexes and 96 pens which form 48 2-pen combos. It also has 2 pseudofacets shaped like the compound of 3 hexes (AKA "sico = stellated ico, which is the dual of gico from the ico regiment).

1291. Ihsiap - (ISS e yap) invertihollostellicosatetrachoron antiprism. It has 48 hexes, 48 pens, and 48 raps - it is the blend of 3 hins and 3 hans.

1292. Hesirap - (HE sir ap) hollostellicosatetrachoron retroantiprism. It has 48 hexes, 48 pens, and 48 firps - it is the blend of 3 hins and 3 rinahs.


Below shows how the rectates pair up as conjugates.


The following are self conjugates: hosiap, ihsiap, and hesirap.

The following are conjugate pairs: sidtaxhiap-gadtaxhiap.

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