Vertices: | 44 (20[3] + 12[5] + 12[10]) |
Faces: | 60 (darts) |
Edges: | 120 (60 short + 60 long) |
Symmetry: | Full Icosahedral (Ih) |
Dihedral Angle: | acos(−(44+3*sqrt(5))/61) | ≈146.230659756 degrees |
Dual Solid: | Small Ditrigonal Dodecicosidodecahedron |
(values below based on unit-edge-length Small Ditrigonal Dodecicosidodecahedron) |
Short Edge (60): | 3*sqrt(6*(85+31*sqrt(5)))/22 | ≈4.1493745905168598767 |
Long Edge (60): | 3*sqrt(3*(145+62*sqrt(5)))/19 | ≈4.6058429091724452830 |
Dart Length: | 3*sqrt(10*(3517−585*sqrt(5)))/418 | ≈1.0666772275746133833 |
Dart Width: | 3*(3+sqrt(5))/2 | ≈7.8541019662496845446 |
[5]-Vertex Radius (12): | 3*sqrt(5*(25+2*sqrt(5)))/22 | ≈1.6553482804837096024 |
[3]-Vertex Radius (20): | 3*(10*sqrt(3)+sqrt(15))/38 | ≈1.6731703754128570911 |
[10]-Vertex Radius (12): | 3*sqrt(5+2*sqrt(5))/2 | ≈4.6165253057628801039 |
Edge-scribed Radius: | sqrt(6*(5+sqrt(5)))/4 | ≈1.6472782070926638518 |
Inscribed Radius: | 3*sqrt(305*(9+2*sqrt(5)))/122 | ≈1.5762662330971825539 |