Non-Convex Tetrahedral and Octahedral Polyhedra

Non-convex uniform polyhedra featuring tetrahedral and octahedral symmetries, including hemipolyhedra whose faces pass through the center of the figure and stellated variations.

U03 Octahemioctahedron
03 - Octahemioctahedron
V: 12  |  E: 24  |  F: 12
Vertex Config: 3 · 6 · 3⁄2 · 6
Bowers: oho  |  TOCID: O|C
Wythoff: 3⁄2 3 | 3
Kaleido: K08  |  Wenninger: 68
Dual: (Octahemioctacron) Octahemioctacron
U04 Tetrahemihexahedron
04 - Tetrahemihexahedron
V: 6  |  E: 12  |  F: 7
Vertex Config: 3 · 4 · 3⁄2 · 4
Bowers: thah  |  TOCID: T|T
Wythoff: 3⁄2 3 | 2
Kaleido: K09  |  Wenninger: 67
aka: One-sided Heptahedron
Dual: (Tetrahemihexacron) Tetrahemihexacron
U13 Small Cubicuboctahedron
13 - Small Cubicuboctahedron
V: 24  |  E: 48  |  F: 20
Vertex Config: 4 · 8 · 3⁄2 · 8
Bowers: socco  |  TOCID: bCO
Wythoff: 3⁄2 4 | 4
Kaleido: K18  |  Wenninger: 69
Dual: (Small Hexacronic Icositetrahedron) Small Hexacronic Icositetrahedron
U14 Great Cubicuboctahedron
14 - Great Cubicuboctahedron
V: 24  |  E: 48  |  F: 20
Vertex Config: 3 · 8⁄3 · 4 · 8⁄3
Bowers: gocco  |  TOCID: cOC*
Wythoff: 3 4 | 4⁄3
Kaleido: K19  |  Wenninger: 77
Dual: (Great Hexacronic Icositetrahedron) Great Hexacronic Icositetrahedron
U15 Cubohemioctahedron
15 - Cubohemioctahedron
V: 12  |  E: 24  |  F: 10
Vertex Config: 4 · 6 · 4⁄3 · 6
Bowers: cho  |  TOCID: C|O
Wythoff: 4⁄3 4 | 3
Kaleido: K20  |  Wenninger: 78
Dual: (Hexahemioctacron) Hexahemioctacron
U16 Cubotruncated Cuboctahedron
16 - Cubotruncated Cuboctahedron
V: 48  |  E: 72  |  F: 20
Vertex Config: 6 · 8 · 8⁄3
Bowers: cotco  |  TOCID: tCC*
Wythoff: 4⁄3 3 4 |
Kaleido: K21  |  Wenninger: 79
Dual: (Tetradyakis Hexahedron) Tetradyakis Hexahedron
U17 Great Rhombicuboctahedron
17 - Great Rhombicuboctahedron
V: 48  |  E: 72  |  F: 26
Vertex Config: 4 · 4 · 4 · 3⁄2
Bowers: querco  |  TOCID: rOC*
Wythoff: 3⁄2 4 | 2
Kaleido: K22  |  Wenninger: 85
aka: Quasi-rhombicuboctahedron
Dual: (Great Deltoidal Icositetrahedron) Great Deltoidal Icositetrahedron
U18 Small Rhombihexahedron
18 - Small Rhombihexahedron
V: 24  |  E: 48  |  F: 18
Vertex Config: 4 · 8 · 4⁄3 · 8⁄7
Bowers: sroh  |  TOCID: rb|CO
Wythoff: 3⁄2 2 4 |
Kaleido: K23  |  Wenninger: 86
Dual: (Small Rhombihexacron) Small Rhombihexacron
U19 Stellated Truncated Hexahedron
19 - Stellated Truncated Hexahedron
V: 24  |  E: 36  |  F: 14
Vertex Config: 3 · 8⁄3 · 8⁄3
Bowers: quith  |  TOCID: tC*
Wythoff: 2 3 | 4⁄3
Kaleido: K26  |  Wenninger: 92
aka: Quasitruncated Hexahedron
Dual: (Great Triakis Octahedron) Great Triakis Octahedron
U20 Great Truncated Cuboctahedron
20 - Great Truncated Cuboctahedron
V: 48  |  E: 72  |  F: 26
Vertex Config: 4 · 6 · 8⁄3
Bowers: quitco  |  TOCID: tOC*
Wythoff: 2 3 4⁄3 |
Kaleido: K27  |  Wenninger: 93
aka: Quasitruncated Cuboctahedron / Stellatruncated Cuboctahedron
Dual: (Great Disdyakis Dodecahedron) Great Disdyakis Dodecahedron
U21 Great Rhombihexahedron
21 - Great Rhombihexahedron
V: 24  |  E: 48  |  F: 18
Vertex Config: 4 · 8⁄3 · 4⁄3 · 8⁄5
Bowers: groh  |  TOCID: OC*
Wythoff: 2 4⁄3 | 4
Kaleido: K28  |  Wenninger: 103
Dual: (Great Rhombihexacron) Great Rhombihexacron