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Dodecahedron-Icosahedron Compound (Actual)
actual compound
Vertices:
32 (20[3] + 12[5])
Faces:
32 (20 equilateral triangles + 12 regular pentagons)
Edges:
60 (30 short + 30 long)
Symmetry:
Full Icosahedral (Ih)
(values below based on short edge length = 1)
Short Edge (30):
1
Long Edge (30):
(1+sqrt(5))/2
≈1.6180339887498948482
[3]-Vertex Radius (20):
(sqrt(3)+sqrt(15))/4
≈1.4012585384440735447
[5]-Vertex Radius (12):
sqrt(5+2*sqrt(5))/2
≈1.5388417685876267013
Volume:
5*(15+7*sqrt(5))/16
≈9.5788987007807899609
References:
[1]
Dodecahedron-Icosahedron Compound (Wolfram MathWorld)