| Vertices: | 92 (80[3] + 12[5]) |
| Faces: | 60 (mirror-symmetric pentagons) |
| Edges: | 150 (90 short + 60 long) |
| Symmetry: | Chiral Icosahedral (I) |
| Dihedral Angle: | acos(−(2*(x+(2/x))*(1+15*phi)
+(15+16*phi))/209) | ≈153.178732558 degrees |
|
| where: | phi = (1+sqrt(5))/2 |
| x = cbrt((phi+sqrt(phi−5/27))/2)+cbrt((phi−sqrt(phi−5/27))/2) |
|
| Dual Solid: | Snub Dodecahedron (dextro) |
| (values below based on unit-edge-length Snub Dodecahedron) |
| Short Edge (90): | 1/x | ≈0.58289953474498241442 |
| Long Edge (60): | (x*(2+7*phi)+(5*phi−3)+2*(8−3*phi)/x)/31 | ≈1.0199882470228458983 |
| [3]-Vertex Radius (80): | sqrt(3*(x*phi+1+phi+(1/x)))/2 | ≈2.1172098986276657420 |
| [5]-Vertex Radius (12): | sqrt((x^2)*(1009+1067*phi)
+x*(1168+2259*phi)+(1097+941*phi))/62 | ≈2.2200006991613182111 |
| Edge-scribed Radius: | phi*sqrt(x*(x+phi)+1)/2 | ≈2.0970538352520879924 |
| Inscribed Radius: | x*sqrt(209*((x^2)*(104*phi−7)
+x*(52+153*phi)+(195−phi)))/418 | ≈2.0398731549542789999 |
| Volume: | 5*sqrt(x*((x^2)*(287+11405*phi)
+x*(8265+14528*phi)+(13146+2363*phi)))/62 | ≈37.588423673993486442 |