Non-Convex Icosahedral Polyhedra

Non-convex uniform polyhedra exhibiting full or chiral icosahedral symmetry, including star polyhedra, hemipolyhedra, and complex self-intersecting figures.

U30 Small Ditrigonal Icosidodecahedron
30 - Small Ditrigonal Icosidodecahedron
V: 20  |  E: 60  |  F: 32
Vertex Config: 3 · 5⁄2 · 3 · 5⁄2 · 3 · 5⁄2
Bowers: sidtid  |  TOCID: ID*
Wythoff: 3 | 5⁄2 3
Kaleido: K35  |  Wenninger: 70
Dual: (Small Triambic Icosahedron) Small Triambic Icosahedron
U31 Small Icosicosidodecahedron
31 - Small Icosicosidodecahedron
V: 60  |  E: 120  |  F: 52
Vertex Config: 3 · 6 · 5⁄2 · 6
Bowers: siid  |  TOCID: iID*
Wythoff: 5⁄2 3 | 3
Kaleido: K36  |  Wenninger: 71
aka: Small Icosic Icosidodecahedron / Small Icosified Icosidodecahedron
Dual: (Small Icosacronic Hexecontahedron) Small Icosacronic Hexecontahedron
U33 Small Dodecicosidodecahedron
33 - Small Dodecicosidodecahedron
V: 60  |  E: 120  |  F: 44
Vertex Config: 5 · 10 · 3⁄2 · 10
Bowers: saddid  |  TOCID: dID
Wythoff: 3⁄2 5 | 5
Kaleido: K38  |  Wenninger: 72
Dual: (Small Dodecacronic Hexecontahedron) Small Dodecacronic Hexecontahedron
U36 Dodecadodecahedron
36 - Dodecadodecahedron
V: 30  |  E: 60  |  F: 24
Vertex Config: 5 · 5⁄2 · 5 · 5⁄2
Bowers: did  |  TOCID: ED*
Wythoff: 2 | 5⁄2 5
Kaleido: K41  |  Wenninger: 73
Dual: (Medial Rhombic Triacontahedron) Medial Rhombic Triacontahedron
U37 Great Truncated Dodecahedron
37 - Great Truncated Dodecahedron
V: 60  |  E: 90  |  F: 24
Vertex Config: 10 · 10 · 5⁄2
Bowers: tigid  |  TOCID: tE
Wythoff: 2 5⁄2 | 5
Kaleido: K42  |  Wenninger: 75
aka: Truncated Great Dodecahedron
Dual: (Small Stellapentakis Dodecahedron) Small Stellapentakis Dodecahedron
U38 Rhombidodecadodecahedron
38 - Rhombidodecadodecahedron
V: 60  |  E: 120  |  F: 54
Vertex Config: 4 · 5 · 4 · 5⁄2
Bowers: raded  |  TOCID: rED*
Wythoff: 5⁄2 5 | 2
Kaleido: K43  |  Wenninger: 76
Dual: (Medial Deltoidal Hexecontahedron) Medial Deltoidal Hexecontahedron
U39 Small Rhombidodecahedron
39 - Small Rhombidodecahedron
V: 60  |  E: 120  |  F: 42
Vertex Config: 4 · 10 · 4⁄3 · 10⁄9
Bowers: sird  |  TOCID: rd|ID
Wythoff: 2 5⁄2 5 |
Kaleido: K44  |  Wenninger: 74
Dual: (Small Rhombidodecacron) Small Rhombidodecacron
U41 Ditrigonal Dodecadodecahedron
41 - Ditrigonal Dodecadodecahedron
V: 20  |  E: 60  |  F: 24
Vertex Config: 5 · 5⁄3 · 5 · 5⁄3 · 5 · 5⁄3
Bowers: ditdid  |  TOCID: DE*
Wythoff: 3 | 5⁄3 5
Kaleido: K46  |  Wenninger: 80
Dual: (Medial Triambic Icosahedron) Medial Triambic Icosahedron
U42 Great Ditrigonal Dodecicosidodecahedron
42 - Great Ditrigonal Dodecicosidodecahedron
V: 60  |  E: 120  |  F: 44
Vertex Config: 3 · 10⁄3 · 5 · 10⁄3
Bowers: gidditdid  |  TOCID: eJE
Wythoff: 3 5 | 5⁄3
Kaleido: K47  |  Wenninger: 81
aka: Ditrigonary Dodecadodecahedron
Dual: (Great Ditrigonal Dodecacronic Hexecontahedron) Great Ditrigonal Dodecacronic Hexecontahedron
U43 Small Ditrigonal Dodecicosidodecahedron
43 - Small Ditrigonal Dodecicosidodecahedron
V: 60  |  E: 120  |  F: 44
Vertex Config: 3 · 10 · 5⁄3 · 10
Bowers: sidditdid  |  TOCID: dID*
Wythoff: 5⁄3 3 | 5
Kaleido: K48  |  Wenninger: 82
aka: Ditrigonary Dodecadodecahedron
Dual: (Small Ditrigonal Dodecacronic Hexecontahedron) Small Ditrigonal Dodecacronic Hexecontahedron
U44 Icosidodecadodecahedron
44 - Icosidodecadodecahedron
V: 60  |  E: 120  |  F: 44
Vertex Config: 5 · 6 · 5⁄3 · 6
Bowers: ided  |  TOCID: iED*
Wythoff: 5⁄3 5 | 3
Kaleido: K49  |  Wenninger: 83
aka: Icosified Dodecadodecahedron
Dual: (Medial Icosacronic Hexecontahedron) Medial Icosacronic Hexecontahedron
U45 Icositruncated Dodecadodecahedron
45 - Icositruncated Dodecadodecahedron
V: 120  |  E: 180  |  F: 44
Vertex Config: 6 · 10 · 10⁄3
Bowers: itdid  |  TOCID: tDE*
Wythoff: 5⁄3 3 5 |
Kaleido: K50  |  Wenninger: 84
Dual: (Tridyakis Icosahedron) Tridyakis Icosahedron
U47 Great Ditrigonal Icosidodecahedron
47 - Great Ditrigonal Icosidodecahedron
V: 20  |  E: 60  |  F: 32
Vertex Config: (3 · 5 · 3 · 5 · 3 · 5)/2
Bowers: gidtid  |  TOCID: JE
Wythoff: 3⁄2 | 3 5
Kaleido: K52  |  Wenninger: 87
Dual: (Great Triambic Icosahedron) Great Triambic Icosahedron
U48 Great Icosicosidodecahedron
48 - Great Icosicosidodecahedron
V: 60  |  E: 120  |  F: 52
Vertex Config: 5 · 6 · 3⁄2 · 6
Bowers: giid  |  TOCID: iJE
Wythoff: 3⁄2 5 | 3
Kaleido: K53  |  Wenninger: 88
aka: Great Icosified Icosidodecahedron
Dual: (Great Icosacronic Hexecontahedron) Great Icosacronic Hexecontahedron
U49 Small Icosihemidodecahedron
49 - Small Icosihemidodecahedron
V: 30  |  E: 60  |  F: 26
Vertex Config: 3 · 10 · 3⁄2 · 10
Bowers: seihid  |  TOCID: I|D
Wythoff: 3⁄2 3 | 5
Kaleido: K54  |  Wenninger: 89
Dual: (Small Icosihemidodecacron) Small Icosihemidodecacron
U50 Small Dodecicosahedron
50 - Small Dodecicosahedron
V: 60  |  E: 120  |  F: 32
Vertex Config: 6 · 10 · 6⁄5 · 10⁄9
Bowers: siddy  |  TOCID: di|ID*
Wythoff: 5⁄3 5⁄2 3 |
Kaleido: K55  |  Wenninger: 90
Dual: (Small Dodecicosacron) Small Dodecicosacron
U51 Small Dodecahemidodecahedron
51 - Small Dodecahemidodecahedron
V: 30  |  E: 60  |  F: 18
Vertex Config: 5 · 10 · 5⁄4 · 10
Bowers: sidhid  |  TOCID: D|I
Wythoff: 5⁄4 5 | 5
Kaleido: K56  |  Wenninger: 91
Dual: (Small Dodecahemidodecacron) Small Dodecahemidodecacron
U54 Great Icosidodecahedron
54 - Great Icosidodecahedron
V: 30  |  E: 60  |  F: 32
Vertex Config: 3 · 5⁄2 · 3 · 5⁄2
Bowers: gid  |  TOCID: JE*
Wythoff: 3⁄2 5 | 3
Kaleido: K59  |  Wenninger: 94
Dual: (Great Rhombic Triacontahedron) Great Rhombic Triacontahedron
U55 Truncated Great Icosahedron
55 - Truncated Great Icosahedron
V: 60  |  E: 90  |  F: 32
Vertex Config: 6 · 6 · 5⁄2
Bowers: tiggy  |  TOCID: tJ
Wythoff: 2 5⁄2 | 3
Kaleido: K60  |  Wenninger: 95
Dual: (Great Stellapentakis Dodecahedron) Great Stellapentakis Dodecahedron
U56 Rhombicosahedron
56 - Rhombicosahedron
V: 60  |  E: 120  |  F: 50
Vertex Config: 4 · 6⁄5 · 4⁄3 · 6
Bowers: ri  |  TOCID: ri|ED*
Wythoff: 2 5⁄2 3 |
Kaleido: K61  |  Wenninger: 96
Dual: (Rhombicosacron) Rhombicosacron
U58 Small Stellated Truncated Dodecahedron
58 - Small Stellated Truncated Dodecahedron
V: 60  |  E: 90  |  F: 24
Vertex Config: 5 · 10⁄3 · 10⁄3
Bowers: quit sissid  |  TOCID: tD*
Wythoff: 2 5 | 5⁄3
Kaleido: K63  |  Wenninger: 97
aka: Quasitruncated Small Stellated Dodecahedron / Small Stellatruncated Dodecahedron
Dual: (Great Pentakis Dodecahedron) Great Pentakis Dodecahedron
U59 Truncated Dodecadodecahedron
59 - Truncated Dodecadodecahedron
V: 120  |  E: 180  |  F: 54
Vertex Config: 4 · 10 · 10⁄3
Bowers: quitdid  |  TOCID: tED*
Wythoff: 5⁄3 2 5 |
Kaleido: K64  |  Wenninger: 98
aka: Quasitruncated Dodecahedron / Stellatruncated Dodecadodecahedron
Dual: (Medial Disdyakis Triacontahedron) Medial Disdyakis Triacontahedron
U61 Great Dodecicosidodecahedron
61 - Great Dodecicosidodecahedron
V: 60  |  E: 120  |  F: 44
Vertex Config: 3 · 10⁄3 · 5⁄2 · 10⁄3
Bowers: gaddid  |  TOCID: eJE*
Wythoff: 5⁄2 3 | 5⁄3
Kaleido: K66  |  Wenninger: 99
Dual: (Great Dodecacronic Hexecontahedron) Great Dodecacronic Hexecontahedron
U62 Small Dodecahemicosahedron
62 - Small Dodecahemicosahedron
V: 30  |  E: 60  |  F: 22
Vertex Config: 6 · 5⁄3 · 6 · 5⁄2
Bowers: sidhei  |  TOCID: E|D*
Wythoff: 5⁄3 5⁄2 | 3
Kaleido: K67  |  Wenninger: 102
Dual: (Small Dodecahemicosacron) Small Dodecahemicosacron
U63 Great Dodecicosahedron
63 - Great Dodecicosahedron
V: 60  |  E: 120  |  F: 32
Vertex Config: 6 · 10⁄7 · 6⁄5 · 10⁄3
Bowers: giddy  |  TOCID: ei|JE
Wythoff: 5⁄3 5⁄2 3 |
Kaleido: K68  |  Wenninger: 101
Dual: (Great Dodecicosacron) Great Dodecicosacron
U65 Great Dodecahemicosahedron
65 - Great Dodecahemicosahedron
V: 30  |  E: 60  |  F: 22
Vertex Config: 5 · 6 · 5⁄4 · 6
Bowers: gidhei  |  TOCID: D*|E
Wythoff: 5⁄4 5 | 3
Kaleido: K70  |  Wenninger: 100
Dual: (Great Dodecahemicosacron) Great Dodecahemicosacron
U66 Great Stellated Truncated Dodecahedron
66 - Great Stellated Truncated Dodecahedron
V: 60  |  E: 90  |  F: 24
Vertex Config: 3 · 10⁄3 · 10⁄3
Bowers: quit gissid  |  TOCID: tE*
Wythoff: 2 3 | 5⁄3
Kaleido: K71  |  Wenninger: 104
aka: Quasitruncated Great Stellated Dodecahedron / Great Stellatruncated Dodecahedron
Dual: (Great Triakis Icosahedron) Great Triakis Icosahedron
U67 Great Rhombicosidodecahedron
67 - Great Rhombicosidodecahedron
V: 60  |  E: 120  |  F: 62
Vertex Config: 3 · 4 · 5⁄3 · 4
Bowers: qrid  |  TOCID: rJE*
Wythoff: 5⁄3 3 | 2
Kaleido: K72  |  Wenninger: 105
aka: Quasirhombicosidodecahedron
Dual: (Great Deltoidal Hexecontahedron) Great Deltoidal Hexecontahedron
U68 Great Truncated Icosidodecahedron
68 - Great Truncated Icosidodecahedron
V: 120  |  E: 180  |  F: 62
Vertex Config: 4 · 6 · 10⁄3
Bowers: gaquatid  |  TOCID: tJE*
Wythoff: 5⁄3 2 3 |
Kaleido: K73  |  Wenninger: 108
aka: Great Quasitruncated Icosidodecahedron / Stellatruncated Icosidodecahedron
Dual: (Great Disdyakis Triacontahedron) Great Disdyakis Triacontahedron
U70 Great Dodecahemidodecahedron
70 - Great Dodecahemidodecahedron
V: 30  |  E: 60  |  F: 18
Vertex Config: 5⁄2 · 10⁄3 · 5⁄3 · 10⁄3
Bowers: gidhid  |  TOCID: E*|J
Wythoff: 5⁄3 5⁄2 | 5⁄3
Kaleido: K75  |  Wenninger: 107
Dual: (Great Dodecahemidodecacron) Great Dodecahemidodecacron
U71 Great Icosihemidodecahedron
71 - Great Icosihemidodecahedron
V: 30  |  E: 60  |  F: 26
Vertex Config: 3 · 10⁄3 · 3⁄2 · 10⁄3
Bowers: geihid  |  TOCID: J|E*
Wythoff: 3⁄2 3 | 5⁄3
Kaleido: K76  |  Wenninger: 106
Dual: (Great Icosihemidodecacron) Great Icosihemidodecacron
U73 Great Rhombidodecahedron
73 - Great Rhombidodecahedron
V: 60  |  E: 120  |  F: 42
Vertex Config: 4 · 10⁄7 · 4⁄3 · 10⁄3
Bowers: gird  |  TOCID: re|JE*
Wythoff: 3⁄2 5⁄3 2 |
Kaleido: K78  |  Wenninger: 109
Dual: (Great Rhombidodecacron) Great Rhombidodecacron
U75 Great Dirhombicosidodecahedron
75 - Great Dirhombicosidodecahedron
V: 60  |  E: 240  |  F: 124
Vertex Config: (3 · 4 · 5⁄3 · 4 · 3⁄2 · 4 · 5⁄2 · 4)/2
Bowers: gidrid  |  TOCID: SSJE*
Wythoff: | 3⁄2 5⁄3 3 5⁄2
Kaleido: K80  |  Wenninger: 119
aka: Miller's Monster
Dual: (Great Dirhombicosidodecacron) Great Dirhombicosidodecacron