Category 3: Rectates

The polyteron rectates are split up into three categories (sort of like the 4-D cases), two of the regiments are quite large, so they have their own categories (category 4 for the rat regiment, and category 5 for the nit regiment), all others are here. This category includes the duorectate regiment (dot regiment) as well. There are 3 regiments here - rix (oooxo) with 7 members, dot (ooxoo) with 5 members, and rin (ooox'o) with 11 members.
Bad

Rix Regiment

Rix is the rectified hexateron, its members all have hixic symmetry with 15 vertices. The tame ones are rix, firx, cax, and baddix - the others are wild.

25. Rix - rectified hexateron. The symbol is oooxo. It has 6 raps and 6 pens. Its verf is a tepe. This is the 5-D version of rap.

26. Cabnix - (CAB nix) cellibiprismatointercepted hexateron. This is the 5-D version of pinnip. It has 6 raps, 15 tepes, and 10 triddips. Its verf is a inverted tet prism.

27. Firx - (FIRKS) facetorectified hexateron. This polychoron is the 5-D version of firp, it has 6 pens, 15 tepes, and 10 triddips. Its verf is tet retroprism.

28. Cax - (CAKS) cellihexateron. It has 6 firps and 15 tepes. Its verf is a 3/2 antiprism walled faceting of tepe.

29. Baddix - (BAD dix) biprismatodishexateron. It has 6 firps, 6 pens, and 10 triddips. Its verf is a 3/2 antiprism walled faceting of tepe.

30. Cindax - (SIN dax) cellintercepted dishexateron. It has 6 pinnips, 6 pens, and 15 tepes. Its verf a pinnip-verf walled faceting of tepe.

31. Nobax - (NO bax) spinobiprismatohexateron. It has 6 pinnips and 10 triddips. Its verf is a pinnip-verf walled faceting of tepe.

Dot Regiment

Dot is the bitruncated hexateron - or better yet - the dodecateron. All of these have 20 vertices. Dot is tame, bad is feral, the other three are wild.

32. Dot - dodecateron. This polychoron is like deca in some ways, but it isn't the 5-D version of it - but in some ways it is a 5-D version of oct. Its symbol is ooxoo. It has 12 raps. Its verf is a triddip. It has dottic (dodecateron) symmetry.

33. Bad - biprismatododecateron. It has 12 firps and 20 triddips. Its verf is a triddip faceting with 3/2 antiprisms instead of trips. It has dottic symmetry

34. Bend - biprismatointercepted dodecateron. It has 12 pinnips and 20 triddips. Its verf is a triddip faceting with pinnip verfs instead of trips. It has dottic symmetry.

35. Cabbix - (CAB bix) cellibiprismatohexateron. It has 6 raps, 15 opes, and 20 triddips. Its verf is a faceting of triddip with half of the trips.

36. Caddix - (CAD dix) cellidishexateron. It has 6 firps, 6 pinnips, and 15 opes. Its verf is a faceting of triddip with 3 firp verfs and 3 pinnip verfs.

Rin Regiment.

Rin is the rectified penteract, these polytera all have 80 vertices. The first 7 have pentic symmetry, the last 4 have hinnic symmetry. The tame ones are rin, firn, tin, and tinhat - others are wild.

37. Rin - rectified penteract. Its symbol is ooox'o = oooX. It has 10 rits and 32 pens. Its verf is a long tepe. This is the 5-D version of co and rit.

38. Nithit - (NITH it) penteracti32hemi32. It has 10 rits, 32 tips, and 16 decas (which go through the center and are hidden also). Its verf is a long inverted tepe. This is the 5-D version of hinnit.

39. Firn - facetorectified penteract. It has 32 pens, 32 tips, and 16 decas. Its verf is a long tet retroprism. This is the 5-D version of firp.

40. Tin - 32penteract. It has 10 firts and 32 tips. Its verf is a 3/2 antiprism walled tepe faceting.

41. Tinhat - (TIN hat) 32intercepted hemi32. It has 10 firts, 32 pens, and 16 decas. Its verf is a 3/2 antiprism walled tepe faceting.

42. Niddit - (NID dit) penteractidis32. It has 10 hinnits, 32 pens, and 32 tips. Its verf is an inverted trip walled tepe faceting.

43. Noht - (NOTE) penteractihemi32. It has 10 hinnits and 16 decas. Its verf is an inverted trip walled tepe faceting.

44. Nath - penteracti32-16. It has 10 stoes, 32 pens, and 16 tips. Its verf is a capped faceting of tepe with sto-verf walls. This is the 5-D version of sto.

45. Nadoh - (NAY doh) penteractidis16. It has 10 stoes, 16 decas, and 16 tips. Its verf is a faceting of tepe with sto-verf walls.

46. Nah - penteracti16. It has 10 gottoes and 16 tips. Its verf is a spiky tepe faceting with gotto-verf walls. This is the 5-D version of gotto.

47. Natdoh - (NAT doh) penteracti32dis16. It has 10 gottoes, 32 pens, 16 tips, and 16 decas. Its verf is a capped tepe faceting with gotto-verf walls. This one is cool looking!

Conjugates

Below shows how the rectates pair up as conjugates.

Conjugates

The following are self conjugates: all.

The following are conjugate pairs: none.

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