| Vertices: | 182 (120[3] + 30[4] + 20[6] + 12[10]) |
| Faces: | 180 (60 short kites + 60 medium kites + 60 long kites) |
| Edges: | 360 (120 short + 120 medium + 120 long) |
| Symmetry: | Full Icosahedral (Ih) |
| Long Edge Angle: | acos(−(21+sqrt(5))/24) | ≈165.505002883 degrees |
| Medium Edge Angle: | acos(−(15+2*sqrt(5))/20) | ≈166.807000959 degrees |
| Short Edge Angle: | acos(−(25+2*sqrt(5))/30) | ≈169.235920193 degrees |
| (values below based on unit-edge-length Truncated Icosidodecahedron) |
| Short Edge (120): | sqrt(271−12*sqrt(5))/22 | ≈0.71026590334213456264 |
| Medium Edge (120): | sqrt(31−12*sqrt(5))/2 | ≈1.0206841173941284126 |
| Long Edge (120): | sqrt(5*(35+12*sqrt(5)))/10 | ≈1.7583062265998701222 |
| Short Kite Length: | sqrt(15*(85−31*sqrt(5)))/11 | ≈1.3942870166557737040 |
| Short Kite Width: | 1 |
| Medium Kite Length: | 3*sqrt(15*(65+19*sqrt(5)))/55 | ≈2.19017447980650378252 |
| Medium Kite Width: | 1 |
| Long Kite Length: | 2*sqrt(15*(5−sqrt(5)))/5 | ≈2.5755459331956214849 |
| Long Kite Width: | 1 |
| [3]-Vertex Radius (120): | sqrt(31+12*sqrt(5))/2 | ≈3.8023944998512935848 |
| [4]-Vertex Radius (30): | 3*(5+4*sqrt(5))/11 | ≈3.8029832481815887597 |
| [6]-Vertex Radius (20): | sqrt(15) | ≈3.8729833462074168852 |
| [10]-Vertex Radius (12): | 3*sqrt(5*(5+2*sqrt(5)))/5 | ≈4.1291457614135206146 |
| Inscribed Radius: | sqrt(6*(5+2*sqrt(5)))/2 | ≈3.7693771279217166027 |
| Volume: | 30*(27+26*sqrt(5))/11 | ≈232.19391113180326938 |