Symmetric Canonical Self-Dual Dodecahedra
91 total:
7
5 have C2v symmetry:
1
5 have 6 edge lengths:
3
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Self-Dual Dodecahedron #7 (canonical)
Vertices:
12 (2[3] + 2[3] + 2[3] + 4[4] + 2[5])
Faces:
12 (2 equilateral triangles + {2 * 2} isosceles triangles
+ 4 irregular tetragons + 2 mirror-symmetric pentagons)
Edges:
22 (6 different lengths)
Symmetry:
2-fold Pyramidal (C2v)
(Each pentagon is a regular hexagon plus an equilateral triangle)
(values below based on edge-scribed radius = 1)
Edge 1 (2):
12*sqrt(2)/35
≈0.48487322138506115959
Edge 2 (4):
10*sqrt(2)/21
≈0.67343502970147383276
Edge 3 (7):
2*sqrt(2)/3
≈0.94280904158206336587
Edge 4 (4):
6*sqrt(2)/5
≈1.6970562748477140586
Edge 5 (4):
4*sqrt(2)/3
≈1.8856180831641267317
Edge 6 (1):
2*sqrt(2)
≈2.8284271247461900976
Edge-scribed Radius:
1
Volume:
9784/2835
≈3.4511463844797178131