Uniform Nonconvex Solids W67 To W119
Index | Name | Picture | Dual name | Dual picture | Wythoff symbol | Vertex figure | Symmetry group | U# | K# | V | E | F | Faces by type |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
67 | Tetrahemihexahedron | Tetrahemihexacron | 3/23|2 | 4.3/2.4.3 |
Td | U04 | K09 | 6 | 12 | 7 | 4{3}+3{4} | ||
68 | Octahemioctahedron | Octahemioctacron | 3/23|3 | 6.3/2.6.3 |
Oh | U03 | K08 | 12 | 24 | 12 | 8{3}+4{6} | ||
69 | Small cubicuboctahedron | Small hexacronic icositetrahedron | 3/24|4 | 8.3/2.8.4 |
Oh | U13 | K18 | 24 | 48 | 20 | 8{3}+6{4}+6{8} | ||
70 | Small ditrigonal icosidodecahedron | Small triambic icosahedron | 3|5/23 | (5/2.3)3 |
Ih | U30 | K35 | 20 | 60 | 32 | 20{3}+12{5/2} | ||
71 | Small icosicosidodecahedron | Small icosacronic hexecontahedron | 5/23|3 | 6.5/2.6.3 |
Ih | U31 | K36 | 60 | 120 | 52 | 20{3}+12{5/2}+20{6} | ||
72 | Small dodecicosidodecahedron | Small dodecacronic hexecontahedron | 3/25|5 | 10.3/2.10.5 |
Ih | U33 | K38 | 60 | 120 | 44 | 20{3}+12{5}+12{10} | ||
73 | Dodecadodecahedron | Medial rhombic triacontahedron | 2|5/25 | (5/2.5)2 |
Ih | U36 | K41 | 30 | 60 | 24 | 12{5}+12{5/2} | ||
74 | Small rhombidodecahedron | Small rhombidodecacron | 25/25| | 10.4.10/9.4/3 |
Ih | U39 | K44 | 60 | 120 | 42 | 30{4}+12{10} | ||
75 | Truncated great dodecahedron | Small stellapentakis dodecahedron | 25/2|5 | 10.10.5/2 |
Ih | U37 | K42 | 60 | 90 | 24 | 12{5/2}+12{10} | ||
76 | Rhombidodecadodecahedron | Medial deltoidal hexecontahedron | 5/25|2 | 4.5/2.4.5 |
Ih | U38 | K43 | 60 | 120 | 54 | 30{4}+12{5}+12{5/2} | ||
77 | Great cubicuboctahedron | Great hexacronic icositetrahedron | 3 4|4/3 | 8/3.3.8/3.4 |
Oh | U14 | K19 | 24 | 48 | 20 | 8{3}+6{4}+6{8/3} | ||
78 | Cubohemioctahedron | Hexahemioctacron | 4/34|3 | 6.4/3.6.4 |
Oh | U15 | K20 | 12 | 24 | 10 | 6{4}+4{6} | ||
79 | Cubitruncated cuboctahedron (Cuboctatruncated cuboctahedron) |
Tetradyakis hexahedron | 4/33 4| | 8/3.6.8 |
Oh | U16 | K21 | 48 | 72 | 20 | 8{6}+6{8}+6{8/3} | ||
80 | Ditrigonal dodecadodecahedron | Medial triambic icosahedron | 3|5/35 | (5/3.5)3 |
Ih | U41 | K46 | 20 | 60 | 24 | 12{5}+12{5/2 | ||
81 | Great ditrigonal dodecicosidodecahedron | Great ditrigonal dodecacronic hexecontahedron | 3 5|5/3 | 10/3.3.10/3.5 |
Ih | U42 | K47 | 60 | 120 | 44 | 20{3}+12{5}+12{10/3} | ||
82 | Small ditrigonal dodecicosidodecahedron | Small ditrigonal dodecacronic hexecontahedron | 5/33|5 | 10.5/3.10.3 |
Ih | U43 | K48 | 60 | 120 | 44 | 20{3}+12{5/2}+12{10} | ||
83 | Icosidodecadodecahedron | Medial icosacronic hexecontahedron | 5/35|3 | 6.5/3.6.5 |
Ih | U44 | K49 | 60 | 120 | 44 | 12{5}+12{5/2}+20{6} | ||
84 | Icositruncated dodecadodecahedron (Icosidodecatruncated icosidodecahedron) |
Tridyakis icosahedron | 5/33 5| | 10/3.6.10 |
Ih | U45 | K50 | 120 | 180 | 44 | 20{6}+12{10}+12{10/3} | ||
85 | Nonconvex great rhombicuboctahedron (Quasirhombicuboctahedron) |
Great deltoidal icositetrahedron | 3/24|2 | 4.3/2.4.4 |
Oh | U17 | K22 | 24 | 48 | 26 | 8{3}+(6+12){4} | ||
86 | Small rhombihexahedron | Small rhombihexacron | 3/22 4| | 4.8.4/3.8 |
Oh | U18 | K23 | 24 | 48 | 18 | 12{4}+6{8} | ||
87 | Great ditrigonal icosidodecahedron | Great triambic icosahedron | 3/2|3 5 | (5.3.5.3.5.3)/2 |
Ih | U47 | K52 | 20 | 60 | 32 | 20{3}+12{5} | ||
88 | Great icosicosidodecahedron | Great icosacronic hexecontahedron | 3/25|3 | 6.3/2.6.5 |
Ih | U48 | K53 | 60 | 120 | 52 | 20{3}+12{5}+20{6} | ||
89 | Small icosihemidodecahedron | Small icosihemidodecacron | 3/23|5 | 10.3/2.10.3 |
Ih | U49 | K54 | 30 | 60 | 26 | 20{3}+6{10} | ||
90 | Small dodecicosahedron | Small dodecicosacron | 3/23 5| | 10.6.10/9.6/5 |
Ih | U50 | K55 | 60 | 120 | 32 | 20{6}+12{10} | ||
91 | Small dodecahemidodecahedron | Small dodecahemidodecacron | 5/45|5 | 10.5/4.10.5 |
Ih | U51 | K56 | 30 | 60 | 18 | 12{5}+6{10} | ||
92 | Stellated truncated hexahedron (Quasitruncated hexahedron) |
Great triakis octahedron | 2 3|4/3 | 8/3.8/3.3 |
Oh | U19 | K24 | 24 | 36 | 14 | 8{3}+6{8/3} | ||
93 | Great truncated cuboctahedron (Quasitruncated cuboctahedron) |
Great disdyakis dodecahedron | 4/32 3| | 8/3.4.6 |
Oh | U20 | K25 | 48 | 72 | 26 | 12{4}+8{6}+6{8/3} | ||
94 | Great icosidodecahedron | Great rhombic triacontahedron | 2|5/23 | (5/2.3)2 |
Ih | U54 | K59 | 30 | 60 | 32 | 20{3}+12{5/2} | ||
95 | Truncated great icosahedron | Great stellapentakis dodecahedron | 25/2|3 | 6.6.5/2 |
Ih | U55 | K60 | 60 | 90 | 32 | 12{5/2}+20{6} | ||
96 | Rhombicosahedron | Rhombicosacron | 25/23| | 6.4.6/5.4/3 |
Ih | U56 | K61 | 60 | 120 | 50 | 30{4}+20{6} | ||
97 | Small stellated truncated dodecahedron (Quasitruncated small stellated dodecahedron) |
Great pentakis dodecahedron | 2 5|5/3 | 10/3.10/3.5 |
Ih | U58 | K63 | 60 | 90 | 24 | 12{5}+12{10/3} | ||
98 | Truncated dodecadodecahedron (Quasitruncated dodecahedron) |
Medial disdyakis triacontahedron | 5/32 5| | 10/3.4.10 |
Ih | U59 | K64 | 120 | 180 | 54 | 30{4}+12{10}+12{10/3} | ||
99 | Great dodecicosidodecahedron | Great dodecacronic hexecontahedron | 5/23|5/3 | 10/3.5/2.10/3.3 |
Ih | U61 | K66 | 60 | 120 | 44 | 20{3}+12{5/2}+12{10/3 } | ||
100 | Small dodecahemicosahedron | Small dodecahemicosacron | 5/35/2|3 | 6.5/3.6.5/2 |
Ih | U62 | K67 | 30 | 60 | 22 | 12{5/2}+10{6} | ||
101 | Great dodecicosahedron | Great dodecicosacron | 5/35/23| | 6.10/3.6/5.10/7 |
Ih | U63 | K68 | 60 | 120 | 32 | 20{6}+12{10/3} | ||
102 | Great dodecahemicosahedron | Great dodecahemicosacron | 5/45|3 | 6.5/4.6.5 |
Ih | U65 | K70 | 30 | 60 | 22 | 12{5}+10{6} | ||
103 | Great rhombihexahedron | Great rhombihexacron | 4/33/22| | 4.8/3.4/3.8/5 |
Oh | U21 | K26 | 24 | 48 | 18 | 12{4}+6{8/3} | ||
104 | Great stellated truncated dodecahedron (Quasitruncated great stellated dodecahedron) |
Great triakis icosahedron | 2 3|5/3 | 10/3.10/3.3 |
Ih | U66 | K71 | 60 | 90 | 32 | 20{3}+12{10/3} | ||
105 | Nonconvex great rhombicosidodecahedron (Quasirhombicosidodecahedron) |
Great deltoidal hexecontahedron | 5/33|2 | 4.5/3.4.3 |
Ih | U67 | K72 | 60 | 120 | 62 | 20{3}+30{4}+12{5/2} | ||
106 | Great icosihemidodecahedron | Great icosihemidodecacron | 3 3|5/3 | 10/3.3/2.10/3.3 |
Ih | U71 | K76 | 30 | 60 | 26 | 20{3}+6{10/3} | ||
107 | Great dodecahemidodecahedron | Great dodecahemidodecacron | 5/35/2|5/3 | 10/3.5/3.10/3.5/2 |
Ih | U70 | K75 | 30 | 60 | 18 | 12{5/2}+6{10/3} | ||
108 | Great truncated icosidodecahedron (Great quasitruncated icosidodecahedron) |
Great disdyakis triacontahedron | 5/32 3| | 10/3.4.6 |
Ih | U68 | K73 | 120 | 180 | 62 | 30{4}+20{6}+12{10/3} | ||
109 | Great rhombidodecahedron | Great rhombidodecacron | 3/25/32| | 4.10/3.4/3.10/7 |
Ih | U73 | K78 | 60 | 120 | 42 | 30{4}+12{10/3} | ||
110 | Small snub icosicosidodecahedron | Small hexagonal hexecontahedron | |5/23 3 | 3.3.3.3.3.5/2 |
Ih | U32 | K37 | 60 | 180 | 112 | (40+60){3}+12{5/2} | ||
111 | Snub dodecadodecahedron | Medial pentagonal hexecontahedron | |25/25 | 3.3.5/2.3.5 |
I | U40 | K45 | 60 | 150 | 84 | 60{3}+12{5}+12{5/2} | ||
112 | Snub icosidodecadodecahedron | Medial hexagonal hexecontahedron | |5/33 5 | 3.3.3.3.5.5/3 |
I | U46 | K51 | 60 | 180 | 104 | (20+6){3}+12{5}+12{5/2} | ||
113 | Great inverted snub icosidodecahedron | Great inverted pentagonal hexecontahedron | |5/32 3 | 3.3.3.3.5/3 |
I | U69 | K74 | 60 | 150 | 92 | (20+60){3}+12{5/2} | ||
114 | Inverted snub dodecadodecahedron | Medial inverted pentagonal hexecontahedron | |5/32 5 | 3.5/3.3.3.5 |
I | U60 | K65 | 60 | 150 | 84 | 60{3}+12{5}+12{5/2} | ||
115 | Great snub dodecicosidodecahedron | Great hexagonal hexecontahedron | |5/35/23 | 3.5/3.3.5/2.3.3 |
I | U64 | K69 | 60 | 180 | 104 | (20+60){3}+(12+12){5/2} | ||
116 | Great snub icosidodecahedron | Great pentagonal hexecontahedron | |25/25/2 | 3.3.3.3.5/2 |
I | U57 | K62 | 60 | 150 | 92 | (20+60){3}+12{5/2} | ||
117 | Great retrosnub icosidodecahedron | Great pentagrammic hexecontahedron | |3/25/32 | (3.3.3.3.5/3)/2 |
I | U74 | K79 | 60 | 150 | 92 | (20+60){3}+12{5/2} | ||
118 | Small retrosnub icosicosidodecahedron | Small hexagrammic hexecontahedron | |3/23/25/2 | (3.3.3.3.3.5/2)/2 |
Ih | U72 | K77 | 180 | 60 | 112 | (40+60){3}+12{5/2} | ||
119 | Great dirhombicosidodecahedron | Great dirhombicosidodecacron | |3/25/335/2 | Ih | U75 | K80 | 60 | 240 | 124 | 40{3}+60{4}+24{5/2} |
Read more about this topic: List Of Wenninger Polyhedron Models
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