| Vertices: | 60 (60[6]) |
| Faces: | 104 (80 equilateral triangles + 12 regular pentagons
+ 12 regular pentagrams) |
| Edges: | 180 |
| Symmetry: | Chiral Icosahedral (I) |
| Pentagram-Triangle Angle: | acos(sqrt(root[91125*(x^6)−425250*(x^5)
+888975*(x^4)−607500*(x^3)
+53955*(x^2)−690*x+3481])) | ≈7.352138644 degrees |
| Pentagon-Triangle Angle: | acos(−sqrt(root[91125*(x^6)−425250*(x^5)
+888975*(x^4)−607500*(x^3)
+53955*(x^2)−690*x+3481])) | ≈120.434012966 degrees |
| Triangle-Triangle Angle: | acos(−(1+cbrt(4*(25+3*sqrt(69)))
+cbrt(4*(25−3*sqrt(69))))/9) | ≈146.781253328 degrees |
| Dual Solid: | Medial Hexagonal Hexecontahedron |
| (values below based on edge length = 1) |
| Circumscribed Radius: | sqrt(6*(16+cbrt(4*(97+3*sqrt(69)))
+cbrt(4*(97−3*sqrt(69)))))/12 | ≈1.12689791279993934351 |
| Midscribed Radius: | sqrt(6*(10+cbrt(4*(97+3*sqrt(69)))
+cbrt(4*(97−3*sqrt(69)))))/12 | ≈1.0099004435452336687 |
| Pentagon Center Radius: | sqrt(root[512000*(x^6)−512000*(x^5)
−140800*(x^4)+131200*(x^3)
+17040*(x^2)−5480*x+361]) | ≈0.73911576097583031237 |
| Triangle Center Radius: | sqrt(6*(8+cbrt(4*(97+3*sqrt(69)))
+cbrt(4*(97−3*sqrt(69)))))/12 | ≈0.96776317998750415529 |
| Pentagram Center Radius: | −sqrt(root[512000*(x^6)−512000*(x^5)
−140800*(x^4)+131200*(x^3)
+17040*(x^2)−5480*x+361]) | ≈−0.99674756263701927657 |