Dipyramids & Trapezohedra
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Pentagonal Trapezohedron
Vertices:
12 (10[3] + 2[5])
Faces:
10 (tri-equiangular kites)
Edges:
20 (10 short + 10 long)
Symmetry:
5-fold Antiprismatic (D5v)
Dihedral Angle:
acos(−sqrt(5)/5)
≈116.565051177 degrees
Dual Solid:
Pentagonal Antiprism
(values below based on unit-edge-length Pentagonal Antiprism)
Short Edge (10):
(sqrt(5)−1)/2
≈0.61803398874989484820
Long Edge (10):
(1+sqrt(5))/2
≈1.6180339887498948482
[3]-Vertex Radius (10):
sqrt(3)/2
≈0.86602540378443864676
[5]-Vertex Radius (2):
sqrt(5+2*sqrt(5))/2
≈1.5388417685876267013
Edge-scribed Radius:
(1+sqrt(5))/4
≈0.80901699437494742410
Inscribed Radius:
sqrt(5*(5+2*sqrt(5)))/10
≈0.68819096023558676910
Volume:
5*(3+sqrt(5))/12
≈2.181694990624912373504