# List of Wenninger polyhedron models

This is an indexed list of the uniform and stellated polyhedra from the book Polyhedron Models, by Magnus Wenninger.
The book was written as a guide book to building polyhedra as physical models. It includes templates of face elements for construction and helpful hints in building, and also brief descriptions on the theory behind these shapes. It contains the 75 nonprismatic uniform polyhedra, as well as 44 stellated forms of the convex regular and quasiregular polyhedra.
Models listed here can be cited as "Wenninger Model Number N", or W$_N$ for brevity.
The polyhedra are grouped in 5 tables: Regular (1–5), Semiregular (6–18), regular star polyhedra (20–22,41), Stellations and compounds (19–66), and uniform star polyhedra (67–119). The four regular star polyhedra are listed twice because they belong to both the uniform polyhedra and stellation groupings.

## Platonic solids (regular convex polyhedra) W1 to W5

| Index | Name | Dual name | Wythoff symbol | Vertex figure and Schläfli symbol | Symmetry group | U# | K# | V | E | F | Faces by type |
| 1 | Tetrahedron | Tetrahedron | 3|2 3 | {3,3} | T$_d$ | U01 | K06 | 4 | 6 | 4 | 4{3} |
| 2 | Octahedron | Hexahedron | 4|2 3 | {3,4} | O$_h$ | U05 | K10 | 6 | 12 | 8 | 8{3} |
| 3 | Hexahedron (Cube) | Octahedron | 3|2 4 | {4,3} | O$_h$ | U06 | K11 | 8 | 12 | 6 | 6{4} |
| 4 | Icosahedron | Dodecahedron | 5|2 3 | {3,5} | I$_h$ | U22 | K27 | 12 | 30 | 20 | 20{3} |
| 5 | Dodecahedron | Icosahedron | 3|2 5 | {5,3} | I$_h$ | U23 | K28 | 20 | 30 | 12 | 12{5} |

## Archimedean solids (Semiregular) W6 to W18

| Index | Name | Dual name | Wythoff symbol | Vertex figure | Symmetry group | U# | K# | V | E | F | Faces by type |
| 6 | Truncated tetrahedron | triakis tetrahedron | 2 3|3 | 3.6.6 | T$_d$ | U02 | K07 | 12 | 18 | 8 | 4{3} + 4{6} |
| 7 | Truncated octahedron | tetrakis hexahedron | 2 4|3 | 4.6.6 | O$_h$ | U08 | K13 | 14 | 36 | 24 | 6{4} + 8{6} |
| 8 | Truncated hexahedron | triakis octahedron | 2 3|4 | 3.8.8 | O$_h$ | U09 | K14 | 24 | 36 | 14 | 8{3} + 6{8} |
| 9 | Truncated icosahedron | pentakis dodecahedron | 2 5|3 | 5.6.6 | I$_h$ | U25 | K30 | 60 | 90 | 32 | 12{5} + 20{6} |
| 10 | Truncated dodecahedron | triakis icosahedron | 2 3|5 | 3.10.10 | I$_h$ | U26 | K31 | 60 | 90 | 32 | 20{3} + 12{10} |
| 11 | Cuboctahedron | rhombic dodecahedron | 2|3 4 | 3.4.3.4 | O$_h$ | U07 | K12 | 12 | 24 | 14 | 8{3} + 6{4} |
| 12 | Icosidodecahedron | rhombic triacontahedron | 2|3 5 | 3.5.3.5 | I$_h$ | U24 | K29 | 30 | 60 | 32 | 20{3} + 12{5} |
| 13 | Small rhombicuboctahedron | deltoidal icositetrahedron | 3 4|2 | 3.4.4.4 | O$_h$ | U10 | K15 | 24 | 48 | 26 | 8{3}+(6+12){4} |
| 14 | Small rhombicosidodecahedron | deltoidal hexecontahedron | 3 5|2 | 3.4.5.4 | I$_h$ | U27 | K32 | 60 | 120 | 62 | 20{3} + 30{4} + 12{5} |
| 15 | Truncated cuboctahedron (Great rhombicuboctahedron) | disdyakis dodecahedron | 2 3 4| | 4.6.8 | O$_h$ | U11 | K16 | 48 | 72 | 26 | 12{4} + 8{6} + 6{8} |
| 16 | Truncated icosidodecahedron (Great rhombicosidodecahedron) | disdyakis triacontahedron | 2 3 5| | 4.6.10 | I$_h$ | U28 | K33 | 120 | 180 | 62 | 30{4} + 20{6} + 12{10} |
| 17 | Snub cube | pentagonal icositetrahedron | |2 3 4 | 3.3.3.3.4 | O | U12 | K17 | 24 | 60 | 38 | (8 + 24){3} + 6{4} |
| 18 | Snub dodecahedron | pentagonal hexecontahedron | |2 3 5 | 3.3.3.3.5 | I | U29 | K34 | 60 | 150 | 92 | (20 + 60){3} + 12{5} |

## Kepler–Poinsot polyhedra (Regular star polyhedra) W20, W21, W22 and W41

| Index | Name | Dual name | Wythoff symbol | Vertex figure and Schläfli symbol | Symmetry group | U# | K# | V | E | F | Faces by type |
| 20 | Small stellated dodecahedron | Great dodecahedron | 5|2$^5$/$_2$ | {$^5$/$_2$,5} | I$_h$ | U34 | K39 | 12 | 30 | 12 | 12{$^5$/$_2$} |
| 21 | Great dodecahedron | Small stellated dodecahedron | $^5$/$_2$|2 5 | {5,$^5$/$_2$} | I$_h$ | U35 | K40 | 12 | 30 | 12 | 12{5} |
| 22 | Great stellated dodecahedron | Great icosahedron | 3|2$^5$/$_2$ | {$^5$/$_2$,3} | I$_h$ | U52 | K57 | 20 | 30 | 12 | 12{$^5$/$_2$} |
| 41 | Great icosahedron (16th stellation of icosahedron) | Great stellated dodecahedron | $^5$/$_2$|2 3 | {3,$^5$/$_2$} | I$_h$ | U53 | K58 | 12 | 30 | 20 | 20{3} |

## Stellations: models W19 to W66
### Stellations of octahedron

| Index | Name | Symmetry group | Picture | Facets |
| 2 | Octahedron (regular) | O$_h$ | | |
| 19 | Stellated octahedron (Compound of two tetrahedra) | O$_h$ | | |

### Stellations of dodecahedron

| Index | Name | Symmetry group |
| 5 | Dodecahedron (regular) | I$_h$ |
| 20 | Small stellated dodecahedron (regular) (First stellation of dodecahedron) | I$_h$ |
| 21 | Great dodecahedron (regular) (Second stellation of dodecahedron) | I$_h$ |
| 22 | Great stellated dodecahedron (regular) (Third stellation of dodecahedron) | I$_h$ |

### Stellations of icosahedron

| Index | Name | Symmetry group |
| 4 | Icosahedron (regular) | I$_h$ |
| 23 | Compound of five octahedra (First compound stellation of icosahedron) | I$_h$ |
| 24 | Compound of five tetrahedra (Second compound stellation of icosahedron) | I |
| 25 | Compound of ten tetrahedra (Third compound stellation of icosahedron) | I$_h$ |
| 26 | Small triambic icosahedron (First stellation of icosahedron) (Triakis icosahedron) | I$_h$ |
| 27 | Second stellation of icosahedron | I$_h$ |
| 28 | Excavated dodecahedron (Third stellation of icosahedron) | I$_h$ |
| 29 | Fourth stellation of icosahedron | I$_h$ |
| 30 | Fifth stellation of icosahedron | I$_h$ |
| 31 | Sixth stellation of icosahedron | I$_h$ |
| 32 | Seventh stellation of icosahedron | I$_h$ |
| 33 | Eighth stellation of icosahedron | I$_h$ |
| 34 | Ninth stellation of icosahedron Great triambic icosahedron | I$_h$ |
| 35 | Tenth stellation of icosahedron | I |
| 36 | Eleventh stellation of icosahedron | I |
| 37 | Twelfth stellation of icosahedron | I$_h$ |
| 38 | Thirteenth stellation of icosahedron | I |
| 39 | Fourteenth stellation of icosahedron | I |
| 40 | Fifteenth stellation of icosahedron | I |
| 41 | Great icosahedron (regular) (Sixteenth stellation of icosahedron) | I$_h$ |
| 42 | Final stellation of the icosahedron | I$_h$ |

### Stellations of cuboctahedron

| Index | Name | Symmetry group |
| 11 | Cuboctahedron (regular) | O$_h$ |
| 43 | Compound of cube and octahedron (First stellation of cuboctahedron) | O$_h$ |
| 44 | Second stellation of cuboctahedron | O$_h$ |
| 45 | Third stellation of cuboctahedron | O$_h$ |
| 46 | Fourth stellation of cuboctahedron | O$_h$ |

### Stellations of icosidodecahedron

| Index | Name | Symmetry group |
| 12 | Icosidodecahedron (regular) | I$_h$ |
| 47 | (First stellation of icosidodecahedron) Compound of dodecahedron and icosahedron | I$_h$ |
| 48 | Second stellation of icosidodecahedron | I$_h$ |
| 49 | Third stellation of icosidodecahedron | I$_h$ |
| 50 | Fourth stellation of icosidodecahedron (Compound of small stellated dodecahedron and triakis icosahedron) | I$_h$ |
| 51 | Fifth stellation of icosidodecahedron (Compound of small stellated dodecahedron and five octahedra) | I$_h$ |
| 52 | Sixth stellation of icosidodecahedron | I$_h$ |
| 53 | Seventh stellation of icosidodecahedron | I$_h$ |
| 54 | Eighth stellation of icosidodecahedron (Compound of five tetrahedra and great dodecahedron) | I |
| 55 | Ninth stellation of icosidodecahedron | I$_h$ |
| 56 | Tenth stellation of icosidodecahedron | I$_h$ |
| 57 | Eleventh stellation of icosidodecahedron | I$_h$ |
| 58 | Twelfth stellation of icosidodecahedron | I$_h$ |
| 59 | Thirteenth stellation of icosidodecahedron | I$_h$ |
| 60 | Fourteenth stellation of icosidodecahedron | I$_h$ |
| 61 | Compound of great stellated dodecahedron and great icosahedron | I$_h$ |
| 62 | Fifteenth stellation of icosidodecahedron | I$_h$ |
| 63 | Sixteenth stellation of icosidodecahedron | I$_h$ |
| 64 | Seventeenth stellation of icosidodecahedron | I$_h$ |
| 65 | Eighteenth stellation of icosidodecahedron | I$_h$ |
| 66 | Nineteenth stellation of icosidodecahedron | I$_h$ |

## Uniform nonconvex solids W67 to W119

| Index | Name | Dual name | Wythoff symbol | Vertex figure | Symmetry group | U# | K# | V | E | F | Faces by type |
| 67 | Tetrahemihexahedron | Tetrahemihexacron | $^3$/$_2$3|2 | 4.$^3$/$_2$.4.3 | T$_d$ | U04 | K09 | 6 | 12 | 7 | 4{3}+3{4} |
| 68 | Octahemioctahedron | Octahemioctacron | $^3$/$_2$3|3 | 6.$^3$/$_2$.6.3 | O$_h$ | U03 | K08 | 12 | 24 | 12 | 8{3}+4{6} |
| 69 | Small cubicuboctahedron | Small hexacronic icositetrahedron | $^3$/$_2$4|4 | 8.$^3$/$_2$.8.4 | O$_h$ | U13 | K18 | 24 | 48 | 20 | 8{3}+6{4}+6{8} |
| 70 | Small ditrigonal icosidodecahedron | Small triambic icosahedron | 3|$^5$/$_2$3 | ($^5$/$_2$.3)$^3$ | I$_h$ | U30 | K35 | 20 | 60 | 32 | 20{3}+12{$^5$/$_2$} |
| 71 | Small icosicosidodecahedron | Small icosacronic hexecontahedron | $^5$/$_2$3|3 | 6.$^5$/$_2$.6.3 | I$_h$ | U31 | K36 | 60 | 120 | 52 | 20{3}+12{$^5$/$_2$}+20{6} |
| 72 | Small dodecicosidodecahedron | Small dodecacronic hexecontahedron | $^3$/$_2$5|5 | 10.$^3$/$_2$.10.5 | I$_h$ | U33 | K38 | 60 | 120 | 44 | 20{3}+12{5}+12{10} |
| 73 | Dodecadodecahedron | Medial rhombic triacontahedron | 2|$^5$/$_2$5 | ($^5$/$_2$.5)$^2$ | I$_h$ | U36 | K41 | 30 | 60 | 24 | 12{5}+12{$^5$/$_2$} |
| 74 | Small rhombidodecahedron | Small rhombidodecacron | 2$^5$/$_2$5| | 10.4.$^{10}$/$_9$.$^4$/$_3$ | I$_h$ | U39 | K44 | 60 | 120 | 42 | 30{4}+12{10} |
| 75 | Truncated great dodecahedron | Small stellapentakis dodecahedron | 2$^5$/$_2$|5 | 10.10.$^5$/$_2$ | I$_h$ | U37 | K42 | 60 | 90 | 24 | 12{$^5$/$_2$}+12{10} |
| 76 | Rhombidodecadodecahedron | Medial deltoidal hexecontahedron | $^5$/$_2$5|2 | 4.$^5$/$_2$.4.5 | I$_h$ | 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 | O$_h$ | U14 | K19 | 24 | 48 | 20 | 8{3}+6{4}+6{$^8$/$_3$} |
| 78 | Cubohemioctahedron | Hexahemioctacron | $^4$/$_3$4|3 | 6.$^4$/$_3$.6.4 | O$_h$ | U15 | K20 | 12 | 24 | 10 | 6{4}+4{6} |
| 79 | Cubitruncated cuboctahedron (Cuboctatruncated cuboctahedron) | Tetradyakis hexahedron | $^4$/$_3$3 4| | $^8$/$_3$.6.8 | O$_h$ | U16 | K21 | 48 | 72 | 20 | 8{6}+6{8}+6{$^8$/$_3$} |
| 80 | Ditrigonal dodecadodecahedron | Medial triambic icosahedron | 3|$^5$/$_3$5 | ($^5$/$_3$.5)$^3$ | I$_h$ | 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 | I$_h$ | U42 | K47 | 60 | 120 | 44 | 20{3}+12{5}+12{$^{10}$/$_3$} |
| 82 | Small ditrigonal dodecicosidodecahedron | Small ditrigonal dodecacronic hexecontahedron | $^5$/$_3$3|5 | 10.$^5$/$_3$.10.3 | I$_h$ | U43 | K48 | 60 | 120 | 44 | 20{3}+12{$^5$/$_2$}+12{10} |
| 83 | Icosidodecadodecahedron | Medial icosacronic hexecontahedron | $^5$/$_3$5|3 | 6.$^5$/$_3$.6.5 | I$_h$ | U44 | K49 | 60 | 120 | 44 | 12{5}+12{$^5$/$_2$}+20{6} |
| 84 | Icositruncated dodecadodecahedron (Icosidodecatruncated icosidodecahedron) | Tridyakis icosahedron | $^5$/$_3$3 5| | $^{10}$/$_3$.6.10 | I$_h$ | U45 | K50 | 120 | 180 | 44 | 20{6}+12{10}+12{$^{10}$/$_3$} |
| 85 | Nonconvex great rhombicuboctahedron (Quasirhombicuboctahedron) | Great deltoidal icositetrahedron | $^3$/$_2$4|2 | 4.$^3$/$_2$.4.4 | O$_h$ | U17 | K22 | 24 | 48 | 26 | 8{3}+(6+12){4} |
| 86 | Small rhombihexahedron | Small rhombihexacron | $^3$/$_2$2 4| | 4.8.$^4$/$_3$.8 | O$_h$ | 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)/$_2$ | I$_h$ | U47 | K52 | 20 | 60 | 32 | 20{3}+12{5} |
| 88 | Great icosicosidodecahedron | Great icosacronic hexecontahedron | $^3$/$_2$5|3 | 6.$^3$/$_2$.6.5 | I$_h$ | U48 | K53 | 60 | 120 | 52 | 20{3}+12{5}+20{6} |
| 89 | Small icosihemidodecahedron | Small icosihemidodecacron | $^3$/$_2$3|5 | 10.$^3$/$_2$.10.3 | I$_h$ | U49 | K54 | 30 | 60 | 26 | 20{3}+6{10} |
| 90 | Small dodecicosahedron | Small dodecicosacron | $^3$/$_2$3 5| | 10.6.$^{10}$/$_9$.$^6$/$_5$ | I$_h$ | U50 | K55 | 60 | 120 | 32 | 20{6}+12{10} |
| 91 | Small dodecahemidodecahedron | Small dodecahemidodecacron | $^5$/$_4$5|5 | 10.$^5$/$_4$.10.5 | I$_h$ | 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 | O$_h$ | U19 | K24 | 24 | 36 | 14 | 8{3}+6{$^8$/$_3$} |
| 93 | Great truncated cuboctahedron (Quasitruncated cuboctahedron) | Great disdyakis dodecahedron | $^4$/$_3$2 3| | $^8$/$_3$.4.6 | O$_h$ | U20 | K25 | 48 | 72 | 26 | 12{4}+8{6}+6{$^8$/$_3$} |
| 94 | Great icosidodecahedron | Great rhombic triacontahedron | 2|$^5$/$_2$3 | ($^5$/$_2$.3)$^2$ | I$_h$ | U54 | K59 | 30 | 60 | 32 | 20{3}+12{$^5$/$_2$} |
| 95 | Truncated great icosahedron | Great stellapentakis dodecahedron | 2$^5$/$_2$|3 | 6.6.$^5$/$_2$ | I$_h$ | U55 | K60 | 60 | 90 | 32 | 12{$^5$/$_2$}+20{6} |
| 96 | Rhombicosahedron | Rhombicosacron | 2$^5$/$_2$3| | 6.4.$^6$/$_5$.$^4$/$_3$ | I$_h$ | 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 | I$_h$ | U58 | K63 | 60 | 90 | 24 | 12{5}+12{$^{10}$/$_3$} |
| 98 | Truncated dodecadodecahedron (Quasitruncated dodecahedron) | Medial disdyakis triacontahedron | $^5$/$_3$2 5| | $^{10}$/$_3$.4.10 | I$_h$ | U59 | K64 | 120 | 180 | 54 | 30{4}+12{10}+12{$^{10}$/$_3$} |
| 99 | Great dodecicosidodecahedron | Great dodecacronic hexecontahedron | $^5$/$_2$3|$^5$/$_3$ | $^{10}$/$_3$.$^5$/$_2$.$^{10}$/$_3$.3 | I$_h$ | U61 | K66 | 60 | 120 | 44 | 20{3}+12{$^5$/$_2$}+12{$^{10}$/$_3$} |
| 100 | Small dodecahemicosahedron | Small dodecahemicosacron | $^5$/$_3$$^5$/$_2$|3 | 6.$^5$/$_3$.6.$^5$/$_2$ | I$_h$ | U62 | K67 | 30 | 60 | 22 | 12{$^5$/$_2$}+10{6} |
| 101 | Great dodecicosahedron | Great dodecicosacron | $^5$/$_3$$^5$/$_2$3| | 6.$^{10}$/$_3$.$^6$/$_5$.$^{10}$/$_7$ | I$_h$ | U63 | K68 | 60 | 120 | 32 | 20{6}+12{$^{10}$/$_3$} |
| 102 | Great dodecahemicosahedron | Great dodecahemicosacron | $^5$/$_4$5|3 | 6.$^5$/$_4$.6.5 | I$_h$ | U65 | K70 | 30 | 60 | 22 | 12{5}+10{6} |
| 103 | Great rhombihexahedron | Great rhombihexacron | $^4$/$_3$$^3$/$_2$2| | 4.$^8$/$_3$.$^4$/$_3$.$^8$/$_5$ | O$_h$ | U21 | K26 | 24 | 48 | 18 | 12{4}+6{$^8$/$_3$} |
| 104 | Great stellated truncated dodecahedron (Quasitruncated great stellated dodecahedron) | Great triakis icosahedron | 2 3|$^5$/$_3$ | $^{10}$/$_3$.$^{10}$/$_3$.3 | I$_h$ | U66 | K71 | 60 | 90 | 32 | 20{3}+12{$^{10}$/$_3$} |
| 105 | Nonconvex great rhombicosidodecahedron (Quasirhombicosidodecahedron) | Great deltoidal hexecontahedron | $^5$/$_3$3|2 | 4.$^5$/$_3$.4.3 | I$_h$ | U67 | K72 | 60 | 120 | 62 | 20{3}+30{4}+12{$^5$/$_2$} |
| 106 | Great icosihemidodecahedron | Great icosihemidodecacron | 3 3|$^5$/$_3$ | $^{10}$/$_3$.$^3$/$_2$.$^{10}$/$_3$.3 | I$_h$ | U71 | K76 | 30 | 60 | 26 | 20{3}+6{$^{10}$/$_3$} |
| 107 | Great dodecahemidodecahedron | Great dodecahemidodecacron | $^5$/$_3$$^5$/$_2$|$^5$/$_3$ | $^{10}$/$_3$.$^5$/$_3$.$^{10}$/$_3$.$^5$/$_2$ | I$_h$ | U70 | K75 | 30 | 60 | 18 | 12{$^5$/$_2$}+6{$^{10}$/$_3$} |
| 108 | Great truncated icosidodecahedron (Great quasitruncated icosidodecahedron) | Great disdyakis triacontahedron | $^5$/$_3$2 3| | $^{10}$/$_3$.4.6 | I$_h$ | U68 | K73 | 120 | 180 | 62 | 30{4}+20{6}+12{$^{10}$/$_3$} |
| 109 | Great rhombidodecahedron | Great rhombidodecacron | $^3$/$_2$$^5$/$_3$2| | 4.$^{10}$/$_3$.$^4$/$_3$.$^{10}$/$_7$ | I$_h$ | U73 | K78 | 60 | 120 | 42 | 30{4}+12{$^{10}$/$_3$} |
| 110 | Small snub icosicosidodecahedron | Small hexagonal hexecontahedron | |$^5$/$_2$3 3 | 3.3.3.3.3.$^5$/$_2$ | I$_h$ | U32 | K37 | 60 | 180 | 112 | (40+60){3}+12{$^5$/$_2$} |
| 111 | Snub dodecadodecahedron | Medial pentagonal hexecontahedron | |2$^5$/$_2$5 | 3.3.$^5$/$_2$.3.5 | I | U40 | K45 | 60 | 150 | 84 | 60{3}+12{5}+12{$^5$/$_2$} |
| 112 | Snub icosidodecadodecahedron | Medial hexagonal hexecontahedron | |$^5$/$_3$3 5 | 3.3.3.3.5.$^5$/$_3$ | I | U46 | K51 | 60 | 180 | 104 | (20+6){3}+12{5}+12{$^5$/$_2$} |
| 113 | Great inverted snub icosidodecahedron | Great inverted pentagonal hexecontahedron | |$^5$/$_3$2 3 | 3.3.3.3.$^5$/$_3$ | I | U69 | K74 | 60 | 150 | 92 | (20+60){3}+12{$^5$/$_2$} |
| 114 | Inverted snub dodecadodecahedron | Medial inverted pentagonal hexecontahedron | |$^5$/$_3$2 5 | 3.$^5$/$_3$.3.3.5 | I | U60 | K65 | 60 | 150 | 84 | 60{3}+12{5}+12{$^5$/$_2$} |
| 115 | Great snub dodecicosidodecahedron | Great hexagonal hexecontahedron | |$^5$/$_3$$^5$/$_2$3 | 3.$^5$/$_3$.3.$^5$/$_2$.3.3 | I | U64 | K69 | 60 | 180 | 104 | (20+60){3}+(12+12){$^5$/$_2$} |
| 116 | Great snub icosidodecahedron | Great pentagonal hexecontahedron | |2$^5$/$_2$$^5$/$_2$ | 3.3.3.3.$^5$/$_2$ | I | U57 | K62 | 60 | 150 | 92 | (20+60){3}+12{$^5$/$_2$} |
| 117 | Great retrosnub icosidodecahedron | Great pentagrammic hexecontahedron | |$^3$/$_2$$^5$/$_3$2 | (3.3.3.3.$^5$/$_2$)/$_2$ | I | U74 | K79 | 60 | 150 | 92 | (20+60){3}+12{$^5$/$_2$} |
| 118 | Small retrosnub icosicosidodecahedron | Small hexagrammic hexecontahedron | |$^3$/$_2$$^3$/$_2$$^5$/$_2$ | (3.3.3.3.3.$^5$/$_2$)/$_2$ | I$_h$ | U72 | K77 | 180 | 60 | 112 | (40+60){3}+12{$^5$/$_2$} |
| 119 | Great dirhombicosidodecahedron | Great dirhombicosidodecacron | |$^3$/$_2$$^5$/$_3$3$^5$/$_2$ | (4.$^5$/$_3$.4.3.4.$^5$/$_2$.4.$^3$/$_2$)/$_2$ | I$_h$ | U75 | K80 | 60 | 240 | 124 | 40{3}+60{4}+24{$^5$/$_2$} |