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01 Tetrahedron Vertices: 4 Edges: 6 Faces: 4 Wythoff symbol: 3|2 3 Symmetry Group: {3, 3, 3} Vertex Configuration: tetrahedral Dual: tetrahedron
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02 Truncated tetrahedron Vertices: 12 Edges: 18 Faces: 8 Wythoff symbol: 2 3|3 Symmetry Group: tetrahedral Vertex Configuration: {6, 6, 3} Dual: triakis tetrahedron
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03 Octahemioctahedron Vertices: 12 Edges: 24 Faces: 12 Wythoff symbol: 3/2 3|3 Symmetry Group: tetrahedral Vertex Configuration: {6, 3/2, 6, 3} Dual: octahemioctacron
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04 Tetrahemihexahedron Vertices: 6 Edges: 12 Faces: 7 Wythoff symbol: 3/2 3|2 Symmetry Group: tetrahedral Vertex Configuration: {4, 3/2, 4, 3} Dual: tetrahemihexacron
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05 Octahedron Vertices: 6 Edges: 12 Faces: 8 Wythoff symbol: 4|2 3 Symmetry Group: octahedral Vertex Configuration: {3, 3, 3, 3} Dual: cube
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06 Cube Vertices: 8 Edges: 12 Faces: 6 Wythoff symbol: 3|2 4 Symmetry Group: octahedral Vertex Configuration: {4, 4, 4} Dual: octahedron
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07 Cuboctahedron Vertices: 12 Edges: 24 Faces: 14 Wythoff symbol: 2|3 4 Symmetry Group: octahedral Vertex Configuration: {3, 4, 3, 4} Dual: rhombic dodecahedron
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08 Truncated octahedron Vertices: 24 Edges: 36 Faces: 14 Wythoff symbol: 2 4|3 Symmetry Group: octahedral Vertex Configuration: {6, 6, 4} Dual: tetrakis hexahedron
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09 Truncated cube Vertices: 24 Edges: 36 Faces: 14 Wythoff symbol: 2 3|4 Symmetry Group: octahedral Vertex Configuration: {8, 8, 3} Dual: triakis octahedron
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10 Rhombicuboctahedron Vertices: 24 Edges: 48 Faces: 26 Wythoff symbol: 3 4|2 Symmetry Group: octahedral Vertex Configuration: {4, 3, 4, 4} Dual: deltoidal icositetrahedron
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11 Truncated cuboctahedron Vertices: 48 Edges: 72 Faces: 26 Wythoff symbol: 2 3 4| Symmetry Group: octahedral Vertex Configuration: {4, 6, 8} Dual: disdyakis dodecahedron
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12 Snub cube Vertices: 24 Edges: 60 Faces: 38 Wythoff symbol: |2 3 4 Symmetry Group: octahedral Vertex Configuration: {3, 3, 3, 3, 4} Dual: pentagonal icositetrahedron
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13 Small cubicuboctahedron Vertices: 24 Edges: 48 Faces: 20 Wythoff symbol: 3/2 4|4 Symmetry Group: octahedral Vertex Configuration: {8, 3/2, 8, 4} Dual: small hexacronic icositetrahedron
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14 Great cubicuboctahedron Vertices: 24 Edges: 48 Faces: 20 Wythoff symbol: 3 4|4/3 Symmetry Group: octahedral Vertex Configuration: {8/3, 3, 8/3, 4} Dual: great hexacronic icositetrahedron
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15 Cubohemioctahedron Vertices: 12 Edges: 24 Faces: 10 Wythoff symbol: 4/3 4|3 Symmetry Group: octahedral Vertex Configuration: {6, 4/3, 6, 4} Dual: hexahemioctacron
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16 Cubitruncated cuboctahedron Vertices: 48 Edges: 72 Faces: 20 Wythoff symbol: 4/3 3 4| Symmetry Group: octahedral Vertex Configuration: {8/3, 6, 8} Dual: tetradyakis hexahedron
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17 Great rhombicuboctahedron Vertices: 24 Edges: 48 Faces: 26 Wythoff symbol: 3/2 4|2 Symmetry Group: octahedral Vertex Configuration: {4, 3/2, 4, 4} Dual: great deltoidal icositetrahedron
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18 Small rhombihexahedron Vertices: 24 Edges: 48 Faces: 18 Wythoff symbol: 3/2 2 4| Symmetry Group: octahedral Vertex Configuration: {8, 4, 8/7, 4/3} Dual: small rhombihexacron
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19 Stellated truncated hexahedron Vertices: 24 Edges: 36 Faces: 14 Wythoff symbol: 2 3|4/3 Symmetry Group: octahedral Vertex Configuration: {8/3, 8/3, 3} Dual: great triakis octahedron
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20 Great truncated cuboctahedron Vertices: 48 Edges: 72 Faces: 26 Wythoff symbol: 4/3 2 3| Symmetry Group: octahedral Vertex Configuration: {8/3, 4, 6} Dual: great disdyakis dodecahedron
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21 Great truncated cuboctahedron Vertices: 24 Edges: 48 Faces: 18 Wythoff symbol: 4/3 3/2 2| Symmetry Group: octahedral Vertex Configuration: {4, 8/3, 4/3, 8/5} Dual: great rhombihexacron
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22 Icosahedron Vertices: 12 Edges: 30 Faces: 20 Wythoff symbol: 5|2 3 Symmetry Group: icosahedral Vertex Configuration: {3, 3, 3, 3, 3} Dual: dodecahedron
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23 Dodecahedron Vertices: 20 Edges: 30 Faces: 12 Wythoff symbol: 3|2 5 Symmetry Group: icosahedral Vertex Configuration: {5, 5, 5} Dual: icosahedron
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24 Icosidodecahedron Vertices: 30 Edges: 60 Faces: 32 Wythoff symbol: 2|3 5 Symmetry Group: icosahedral Vertex Configuration: {3, 5, 3, 5} Dual: rhombic triacontahedron
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25 Truncated icosahedron Vertices: 60 Edges: 90 Faces: 32 Wythoff symbol: 2 5|3 Symmetry Group: icosahedral Vertex Configuration: {6, 6, 5} Dual: pentakis dodecahedron
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26 Truncated dodecahedron Vertices: 60 Edges: 90 Faces: 32 Wythoff symbol: 2 3|5 Symmetry Group: icosahedral Vertex Configuration: {10, 10, 3} Dual: triakis icosahedron
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27 Rhombicosidodecahedron Vertices: 60 Edges: 120 Faces: 62 Wythoff symbol: 3 5|2 Symmetry Group: icosahedral Vertex Configuration: {4, 3, 4, 5} Dual: deltoidal hexecontahedron
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28 Truncated icosidodechedon Vertices: 120 Edges: 180 Faces: 62 Wythoff symbol: 2 3 5| Symmetry Group: icosahedral Vertex Configuration: {4, 6, 10} Dual: disdyakis triacontahedron
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29 Snub dodecahedron Vertices: 60 Edges: 150 Faces: 92 Wythoff symbol: |2 3 5 Symmetry Group: icosahedral Vertex Configuration: {3, 3, 3, 3, 5} Dual: pentagonal hexecontahedron
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30 Small ditrigonal icosidodecahedron Vertices: 20 Edges: 60 Faces: 32 Wythoff symbol: 3|5/2 3 Symmetry Group: icosahedral Vertex Configuration: {5/2, 3, 5/2, 3, 5/2, 3} Dual: small triambic icosahedron
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31 Small icosicosidodecahedron Vertices: 60 Edges: 120 Faces: 52 Wythoff symbol: 5/2 3|3 Symmetry Group: icosahedral Vertex Configuration: {6, 5/2, 6, 3} Dual: small icosacronic hexecontahedron
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32 Small snub icosicosidodecahedron Vertices: 60 Edges: 180 Faces: 112 Wythoff symbol: |5/2 3 3 Symmetry Group: icosahedral Vertex Configuration: {3, 5/2, 3, 3, 3, 3} Dual: small hexagonal hexecontahedron
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33 Small dodecicosidodecahedron Vertices: 60 Edges: 120 Faces: 44 Wythoff symbol: 3/2 5|5 Symmetry Group: icosahedral Vertex Configuration: {10, 3/2, 10, 5} Dual: small dodecacronic hexecontahedron
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34 Small stellated dodecahedron Vertices: 12 Edges: 30 Faces: 12 Wythoff symbol: 5|2 5/2 Symmetry Group: icosahedral Vertex Configuration: {5/2, 5/2, 5/2, 5/2, 5/2} Dual: great dodecahedron
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35 Great dodecahedron Vertices: 12 Edges: 30 Faces: 12 Wythoff symbol: 5/2|2 5 Symmetry Group: icosahedral Vertex Configuration: {5, 5, 5, 5, 5}/2 Dual: small stellated dodecahedron
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36 Dodecadodecahedron Vertices: 30 Edges: 60 Faces: 24 Wythoff symbol: 2|5/2 5 Symmetry Group: icosahedral Vertex Configuration: {5/2, 5, 5/2, 5} Dual: medial rhombic triacontahedron
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37 Truncated great dodecahedron Vertices: 60 Edges: 90 Faces: 24 Wythoff symbol: 2 5/2|5 Symmetry Group: icosahedral Vertex Configuration: {10, 10, 5/2} Dual: small stellapentakis dodecahedron
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38 Rhombidodecadodecahedron Vertices: 60 Edges: 120 Faces: 54 Wythoff symbol: 5/2 5|2 Symmetry Group: icosahedral Vertex Configuration: {4, 5/2, 4, 5} Dual: medial deltoidal hexecontahedron
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39 Small rhombidodecahedron Vertices: 60 Edges: 120 Faces: 42 Wythoff symbol: 2 5/2 5| Symmetry Group: icosahedral Vertex Configuration: {10, 4, 10/9, 4/3} Dual: small rhombidodecacron
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40 Snub dodecadodecahedron Vertices: 60 Edges: 150 Faces: 84 Wythoff symbol: |2 5/2 5 Symmetry Group: icosahedral Vertex Configuration: {3, 3, 5/2, 3, 5} Dual: medial pentagonal hexecontahedron
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41 Ditrigonal dodecadodecahedron Vertices: 20 Edges: 60 Faces: 24 Wythoff symbol: 3|5/3 5 Symmetry Group: icosahedral Vertex Configuration: {5/3, 5, 5/3, 5, 5/3, 5} Dual: medial triambic icosahedron
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42 Great ditrigonal dodecicosidodecahedron Vertices: 60 Edges: 120 Faces: 44 Wythoff symbol: 3 5|5/3 Symmetry Group: icosahedral Vertex Configuration: {10/3, 3, 10/3, 5} Dual: great ditrigonal dodecacronic hexecontahedron
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43 Small ditrigonal dodecicosidodecahedron Vertices: 60 Edges: 120 Faces: 44 Wythoff symbol: 5/3 3|5 Symmetry Group: icosahedral Vertex Configuration: {10, 5/3, 10, 3} Dual: small ditrigonal dodecacronic hexecontahedron
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44 Icosidodecadodecahedron Vertices: 60 Edges: 120 Faces: 44 Wythoff symbol: 5/3 5|3 Symmetry Group: icosahedral Vertex Configuration: {6, 5/3, 6, 5} Dual: medial icosacronic hexecontahedron
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45 Icositruncated dodecadodecahedron Vertices: 120 Edges: 180 Faces: 44 Wythoff symbol: 5/3 3 5| Symmetry Group: icosahedral Vertex Configuration: {10/3, 6, 10} Dual: tridyakis icosahedron
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46 Snub icosidodecadodecahedron Vertices: 60 Edges: 180 Faces: 104 Wythoff symbol: |5/3 3 5 Symmetry Group: icosahedral Vertex Configuration: {3, 5/3, 3, 3, 3, 5} Dual: medial hexagonal hexecontahedron
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47 Great ditrigonal icosidodecahedron Vertices: 20 Edges: 60 Faces: 32 Wythoff symbol: 3/2|3 5 Symmetry Group: icosahedral Vertex Configuration: {3, 5, 3, 5, 3, 5}/2 Dual: great triambic icosahedron
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48 Great icosicosidodecahedron Vertices: 60 Edges: 120 Faces: 52 Wythoff symbol: 3/2 5|3 Symmetry Group: icosahedral Vertex Configuration: {6, 3/2, 6, 5} Dual: great icosacronic hexecontahedron
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49 Small icosihemidodecahedron Vertices: 30 Edges: 60 Faces: 26 Wythoff symbol: 3/2 3|5 Symmetry Group: icosahedral Vertex Configuration: {10, 3/2, 10, 3} Dual: small icosihemidodecacron
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50 Small dodecicosahedron Vertices: 60 Edges: 120 Faces: 32 Wythoff symbol: 3/2 3 5| Symmetry Group: icosahedral Vertex Configuration: {10, 6, 10/9, 6/5} Dual: small dodecicosacron
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51 Small dodecahemidodecahedron Vertices: 30 Edges: 60 Faces: 18 Wythoff symbol: 5/4 5|5 Symmetry Group: icosahedral Vertex Configuration: {10, 5/4, 10, 5} Dual: small dodecahemidodecacron
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52 Great stellated dodecahedron Vertices: 20 Edges: 30 Faces: 12 Wythoff symbol: 3|2 5/2 Symmetry Group: icosahedral Vertex Configuration: {5/2, 5/2, 5/2} Dual: great icosahedron
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53 Great icosahedron Vertices: 12 Edges: 30 Faces: 20 Wythoff symbol: 5/2|2 3 Symmetry Group: icosahedral Vertex Configuration: {3, 3, 3, 3, 3}/2 Dual: great stellated dodecahedron
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54 Great icosidodecahedron Vertices: 30 Edges: 60 Faces: 32 Wythoff symbol: 2|5/2 3 Symmetry Group: icosahedral Vertex Configuration: {5/2, 3, 5/2, 3} Dual: great rhombic triacontahedron
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55 Great truncated icosahedron Vertices: 60 Edges: 90 Faces: 32 Wythoff symbol: 2 5/2|3 Symmetry Group: icosahedral Vertex Configuration: {6, 6, 5/2} Dual: great stellapentakis dodecahedron
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56 Rhombicosahedron Vertices: 60 Edges: 120 Faces: 50 Wythoff symbol: 2 5/2 3| Symmetry Group: icosahedral Vertex Configuration: {6, 4, 6/5, 4/3} Dual: rhombicosacron
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57 Great snub icosidodecahedron Vertices: 60 Edges: 150 Faces: 92 Wythoff symbol: |2 5/2 3 Symmetry Group: icosahedral Vertex Configuration: {3, 3, 5/2, 3, 3} Dual: great pentagonal hexecontahedron
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58 Small stellated truncated dodecahedron Vertices: 60 Edges: 90 Faces: 24 Wythoff symbol: 2 5|5/3 Symmetry Group: icosahedral Vertex Configuration: {10/3, 10/3, 5} Dual: great pentakis dodecahedron
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59 Truncated dodecadodecahedron Vertices: 120 Edges: 180 Faces: 54 Wythoff symbol: 5/3 2 5| Symmetry Group: icosahedral Vertex Configuration: {10/3, 4, 10} Dual: medial disdyakis triacontahedron
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60 Inverted snub dodecadodecahedron Vertices: 60 Edges: 150 Faces: 84 Wythoff symbol: |5/3 2 5 Symmetry Group: icosahedral Vertex Configuration: {3, 5/3, 3, 3, 5} Dual: medial inverted pentagonal hexecontahedron
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61 Great dodecicosidodecahedron Vertices: 60 Edges: 120 Faces: 44 Wythoff symbol: 5/2 3|5/3 Symmetry Group: icosahedral Vertex Configuration: {10/3, 5/2, 10/3, 3} Dual: great dodecacronic hexecontahedron
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62 Small dodecahemicosahedron Vertices: 30 Edges: 60 Faces: 22 Wythoff symbol: 5/3 5/2|3 Symmetry Group: icosahedral Vertex Configuration: {6, 5/3, 6, 5/2} Dual: small dodecahemicosacron
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63 Great dodecicosahedron Vertices: 60 Edges: 120 Faces: 32 Wythoff symbol: 5/3 5/2 3| Symmetry Group: icosahedral Vertex Configuration: {6, 10/3, 6/5, 10/7} Dual: great dodecicosacron
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64 Great snub dodecicosidodecahedron Vertices: 60 Edges: 180 Faces: 104 Wythoff symbol: |5/3 5/2 3 Symmetry Group: icosahedral Vertex Configuration: {3, 5/3, 3, 5/2, 3, 3} Dual: great hexagonal hexecontahedron
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65 Great dodecahemicosahedron Vertices: 30 Edges: 60 Faces: 22 Wythoff symbol: 5/4 5|3 Symmetry Group: icosahedral Vertex Configuration: {6, 5/4, 6, 5} Dual: great dodecahemicosacron
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66 Great stellated truncated dodecahedron Vertices: 60 Edges: 90 Faces: 32 Wythoff symbol: 2 3|5/3 Symmetry Group: icosahedral Vertex Configuration: {10/3, 10/3, 3} Dual: great triakis icosahedron
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67 Great rhombicosidodecahedron Vertices: 60 Edges: 120 Faces: 62 Wythoff symbol: 5/3 3|2 Symmetry Group: icosahedral Vertex Configuration: {4, 5/3, 4, 3} Dual: great deltoidal hexecontahedron
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68 Great truncated icosidodecahedron Vertices: 120 Edges: 180 Faces: 62 Wythoff symbol: 5/3 2 3| Symmetry Group: icosahedral Vertex Configuration: {10/3, 4, 6} Dual: great disdyakis triacontahedron
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69 Great inverted snub icosidodecahedron Vertices: 60 Edges: 150 Faces: 92 Wythoff symbol: |5/3 2 3 Symmetry Group: icosahedral Vertex Configuration: {3, 5/3, 3, 3, 3} Dual: great inverted pentagonal hexecontahedron
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70 Great dodecahemidodecahedron Vertices: 30 Edges: 60 Faces: 18 Wythoff symbol: 5/3 5/2|5/3 Symmetry Group: icosahedral Vertex Configuration: {10/3, 5/3, 10/3, 5/2} Dual: great dodecahemidodecacron
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71 Great icosihemidodecahedron Vertices: 30 Edges: 60 Faces: 26 Wythoff symbol: 3/2 3|5/3 Symmetry Group: icosahedral Vertex Configuration: {10/3, 3/2, 10/3, 3} Dual: great icosihemidodecacron
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72 Small retrosnub icosicosidodecahedron Vertices: 60 Edges: 180 Faces: 112 Wythoff symbol: |3/2 3/2 5/2 Symmetry Group: icosahedral Vertex Configuration: {3, 3/2, 3, 3/2, 3, 5/2} Dual: small hexagrammic hexecontahedron
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73 Great rhombidodecahedron Vertices: 60 Edges: 120 Faces: 42 Wythoff symbol: 3/2 5/3 2| Symmetry Group: icosahedral Vertex Configuration: {4, 10/3, 4/3, 10/7} Dual: great rhombidodecacron
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74 Great retrosnub icosidodecahedron Vertices: 60 Edges: 150 Faces: 92 Wythoff symbol: |3/2 5/3 2 Symmetry Group: icosahedral Vertex Configuration: {3, 3/2, 3, 5/3, 3} Dual: great pentagrammic hexecontahedron
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75 Great dirhombicosidodecahedron Vertices: 60 Edges: 240 Faces: 124 Wythoff symbol: |3/2 5/3 3 5/2 Symmetry Group: icosahedral Vertex Configuration: {4, 5/3, 4, 3, 4, 5/2, 4, 3/2} Dual: great dirhombicosidodecacron
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76 Pentagonal prism Vertices: 10 Edges: 15 Faces: 7 Wythoff symbol: 2 5|2 Symmetry Group: dihedral Vertex Configuration: {4, 4, 5} Dual: pentagonal dipyramid
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77 Pentagonal antiprism Vertices: 10 Edges: 20 Faces: 12 Wythoff symbol: |2 2 5 Symmetry Group: dihedral Vertex Configuration: {3, 3, 3, 5} Dual: pentagonal trapezohedron
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78 Pentagrammic prism Vertices: 10 Edges: 15 Faces: 7 Wythoff symbol: 2 5/2|2 Symmetry Group: dihedral Vertex Configuration: {4, 4, 5/2} Dual: pentagrammic dipyramid
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79 Pentagrammic antiprism Vertices: 10 Edges: 20 Faces: 12 Wythoff symbol: |2 2 5/2 Symmetry Group: dihedral Vertex Configuration: {3, 3, 3, 5/2} Dual: pentagrammic deltahedron
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80 Pentagrammic crossed antiprism Vertices: 10 Edges: 20 Faces: 12 Wythoff symbol: |2 2 5/3 Symmetry Group: dihedral Vertex Configuration: {3, 3, 3, 5/3} Dual: pentagrammic concave deltahedron
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