| Vertices: | 152 (20[3] + 60[3] + 60[5] + 12[5]) |
| Faces: | 150 (60 kites + 90 rhombi) |
| Edges: | 300 (240 short + 60 long) |
| Symmetry: | Chiral Icosahedral (I) |
| Long Edge Angle: | acos(−(1−phi+(phi^3)/x)/2) | ≈157.756587464 degrees |
| Short Edge Angle: | acos(−((x^2)−1)/2) | ≈166.306414670 degrees |
|
| where: | phi = (1+sqrt(5))/2 |
| x = cbrt((phi+sqrt(phi−5/27))/2)+cbrt((phi−sqrt(phi−5/27))/2) |
|
| (values below based on unit-edge-length Snub Dodecahedron) |
| Short Edge (240): | sqrt((x^2)+1)/(2*x) | ≈0.578742573949315776654 |
| Long Edge (60): | sqrt(2*(x^2)*(24+53*phi)
+x*(207+337*phi)+(1097−20*phi))/62 | ≈0.88361095303943028718 |
| Rhombus Length: | 1 |
| Rhombus Width: | 1/x | ≈0.58289953474498241442 |
| Kite Length: | (x*(2+7*phi)+(5*phi−3)+2*(8−3*phi)/x)/31 | ≈1.0199882470228458983 |
| Kite Width: | 1 |
| [3]-Vertex Radius (20): | sqrt(3*(x*phi+1+phi+(1/x)))/2 | ≈2.1172098986276657420 |
| [3]-Vertex Radius (60): | sqrt(3*(x*phi+1+phi+(1/x)))/2 | ≈2.1172098986276657420 |
| [5]-Vertex Radius (60): | phi*sqrt(x*(x+phi)+(3−phi))/2 | ≈2.1558373751156397018 |
| [5]-Vertex Radius (12): | sqrt((x^2)*(1009+1067*phi)
+x*(1168+2259*phi)+(1097+941*phi))/62 | ≈2.2200006991613182111 |
| Inscribed Radius: | phi*sqrt(x*(x+phi)+1)/2 | ≈2.0970538352520879924 |
| Volume: | 5*sqrt(3*(x^2)*(8951*phi−3399)
+x*(8460+32617*phi)+5*(10847−1793*phi))/62 | ≈39.725278226867477520 |