| 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))*(15*phi+1)
+(16*phi+15))/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 (laevo) |
| (values below based on unit-edge-length Snub Dodecahedron) |
| Short Edge (90): | 1/x | ≈0.58289953474498241442 |
| Long Edge (60): | (x*(7*phi+2)+(5*phi-3)+2*(8-3*phi)/x)/31 | ≈1.0199882470228458983 |
| [3]-Vertex Radius (80): | sqrt(3*(x*phi+phi+1+(1/x)))/2 | ≈2.1172098986276657420 |
| [5]-Vertex Radius (12): | sqrt((x^2)*(1067*phi+1009)
+x*(2259*phi+1168)+(941*phi+1097))/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*(153*phi+52)+(195-phi)))/418 | ≈2.0398731549542789999 |
| Volume: | 5*sqrt(x*((x^2)*(11405*phi+287)
+x*(14528*phi+8265)+(2363*phi+13146)))/62 | ≈37.588423673993486442 |