| 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 |
| (values below based on edge-scribed radius = 1) |
| Short Edge (90): | 2*sqrt(3−(x^2))/x | ≈0.27796116863872106624 |
| Long Edge (60): | 2*sqrt((x^2)*(218+81*phi)+x*(49*phi−141)
−(23+251*phi))/(31*(x^2)) | ≈0.486391064395460573049 |
| [3]-Vertex Radius (80): | sqrt(3)/x | ≈1.0096116098865696398 |
| [5]-Vertex Radius (12): | sqrt(2*(x^2)*(63*phi−44)+x*(101+183*phi)
+4*(258−151*phi))/31 | ≈1.0586283775087017300 |
| Edge-scribed Radius: | 1 |
| Inscribed Radius: | sqrt(209*(2*((x^2)+2)*(14+phi)
+x*(1+15*phi)))/209 | ≈0.97273285056559586532 |
| Volume: | 20*(−(7+9*phi)+(57−2*phi)/x+2*(3−5*phi)
/(x^2))/31 | ≈4.0759173979281626204 |