Symmetric Canonical Self-Dual Decahedra
28 total:
6
2 have C2v symmetry:
1
5 have 6 edge lengths:
2
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Self-Dual Decahedron #6 (canonical)
Vertices:
10 (2[3] + 4[3] + 2[4] + 2[5])
Faces:
10 (2 isosceles triangles + 4 acute triangles + 2 kites
+ 2 mirror-symmetric pentagons)
Edges:
18 (6 different lengths)
Symmetry:
2-fold Pyramidal (C2v)
(values below based on edge-scribed radius = 1)
Edge 1 (4):
(3*sqrt(10)−5*sqrt(2))/3
≈0.80525505621322091733
Edge 2 (4):
2*(3*sqrt(10)−5*sqrt(2))/5
≈0.96630606745586510080
Edge 3 (1):
2*sqrt(10)/5
≈1.2649110640673517328
Edge 4 (4):
sqrt(10)−sqrt(2)
≈1.7480640977952842832
Edge 5 (4):
4*sqrt(2)/3
≈1.8856180831641267317
Edge 6 (1):
2*sqrt(2)
≈2.8284271247461900976
Edge-scribed Radius:
1
Volume:
8*(13*sqrt(5)−10)/45
≈3.3900237702217361873