Archimedean Solids
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(Uniform #25)
Truncated Icosahedron
canonical form
Vertices:
60 (60[3])
Faces:
32 (12 regular pentagons + 20 regular hexagons)
Edges:
90
Symmetry:
Full Icosahedral (Ih)
Hexagon-Hexagon Angle:
acos(−sqrt(5)/3)
≈138.189685104 degrees
Hexagon-Pentagon Angle:
acos(−sqrt(15*(5+2*sqrt(5)))/15)
≈142.622631859 degrees
Dual Solid:
Pentakis Dodecahedron
(values below based on edge length = 1)
Circumscribed Radius:
sqrt(2*(29+9*sqrt(5)))/4
≈2.4780186590676155376
Midscribed Radius:
3*(1+sqrt(5))/4
≈2.4270509831248422723
Hexagon Center Radius:
(3*sqrt(3)+sqrt(15))/4
≈2.2672839422285121914
Pentagon Center Radius:
sqrt(10*(125+41*sqrt(5)))/20
≈2.3274384367663271103
Volume:
(125+43*sqrt(5))/4
≈55.287730758122739236