Polyhedron Category 4: Trapeziverts

The trapeziverts are grouped into 7 regiments of three. Each regiment contains one with a trapezoid verf, one with a crossed trapezoid verf, and one with a butterfly verf. The butterfly verfed ones are non-orientable, the others are orientable. Some of the non-orientable ones may look different due to neo filling, I'll also have renders of the traditional filling when this is the case. Sirco and srid are convex and therefore are part of the Archimedean solids. The cubic ones (sirco and gocco regiments) have 24 vertices, all others have 60. The co regiment from category 3 could also be included in this category, for they are the trapeziverts with tetrahedral symmetry. They all show up as cells in the uniform polychora. The polychoron categories most similar to this one are 6, 10, 11, 12, 13, 14, 15, 16, 21, and 22.

36. Sirco - (SIR co) small rhombicuboctahedron. Symbol is xo'x. Faces are 6 squares, 8 triangles, and 12 squares.

37. Socco - (SOC co) small cubicuboctahedron. Symbol is (o'x'x,). Faces are 6 squares, 8 triangles, and 6 octagons.

38. Sroh - (SRO) small rhombihexahedron. Faces are 12 squares and 6 octagons.

39. Srid - (SRID) small rhombicosidodecahedron. Symbol is xo^x. Faces are 12 pentagons, 20 triangles, and 30 squares.

40. Saddid - (sa DID) small dodekicosidodecahedron. Symbol is (o^x^x,). Faces are 12 pentagons, 20 triangles, and 12 decagons.

41. Sird - (SIRD) small rhombidodecahedron. Faces are 30 squares and 12 decagons.

42. Raded - (RAY did) rhombidodecadodecahedron. Symbol is x*o^x. Faces are 12 stars, 12 pentagons, and 30 squares.

43. Ided - (I did) icosidodecadodecahedron. Symbol is (x*'o^x). Faces are 12 stars, 12 pentagons, and 20 hexagons.

44. Ri - (RI) rhombicosahedron. Faces are 30 squares and 20 hexagons.

45. Gocco - (GOC co) great cubicuboctahedron. Symbol is (o'x"x). Faces are 6 octagrams, 8 triangles, and 6 squares.

46. Querco - (KWER co) quasirhombicuboctahedron, also called great rhombicuboctahedron. Symbol is xo"x. Faces are 6 squares, 8 triangles, and 12 squares.

47. Groh - (GRO) great rhombihexahedron. Faces are 6 octagrams and 12 squares.

48. Gidditdid - (GID it did) great ditrigonary dodekicosidodecahedron. Symbol is (o^x*'x). Faces are 12 decagrams, 20 triangles, and 12 pentagons.

49. Giid - (GIDE) great icosicosidodecahedron. Symbol is (x,o^x). Faces are 20 triangles, 12 pentagons, and 20 hexagons.

50. Giddy - (GID dee) great dodekicosahedron. Faces are 12 decagrams and 20 hexagons.

51. Siid - (SIDE) small icosicosidodecahedron. Symbol is (xo*x). Faces are 12 stars, 20 triangles, and 20 hexagons.

52. Sidditdid - (SID it did) small ditrigonary dodekicosidodecahedron. Symbol is (o*'x^x). Faces are 12 stars, 20 triangles, and 12 decagons.

53. Siddy - (SID dee) small dodekicosahedron. Faces are 20 hexagons and 12 decagons.

54. Gaddid - (ga DID) great dodekicosidodecahedron. Symbol is (o*x*'x). Faces are 12 stars, 20 triangles, and 12 decagrams.

55. Qrid - (KRID) quasirhombicosidodecahedron, also called great rhombicosidodecahedron. Symbol is xo*'x. Faces are 12 stars, 20 triangles, and 30 squares.

56. Gird - (GIRD) great rhombidodecahedron. Faces are 12 decagrams and 30 squares.

Below are the traditional fillings for groh, giddy, and gird.

Conjugate Pairs: sirco-querco, socco-gocco, sroh-groh, srid-qrid, saddid-gaddid, sird-gird, sidditdid-gidditdid, siid-giid, siddy-giddy.

Self Conjugates: raded, ided, ri.

Category 3: Quasiregulars . . . Polyhedron Page . . . Category 5: Omnitruncates