Symmetric Canonical Self-Dual Decahedra
28 total:
12
10 have C2 symmetry:
1
5 have 6 edge lengths:
4
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(F: faces)
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Self-Dual Decahedron #12 (canonical)
Vertices:
10 (2[3] + 2[3] + 2[4] + 4[4])
Faces:
10 ({2 * 2} isosceles triangles + 2 isosceles trapezoids
+ 4 irregular tetragons)
Edges:
18 (6 different lengths)
Symmetry:
2-fold Cyclic (C2)
(values below based on edge-scribed radius = 1)
Edge 1 (1):
sqrt(sqrt(2)−1)
≈0.64359425290558262474
Edge 2 (4):
sqrt(17*sqrt(2)−23)
≈1.0206030375922931916
Edge 3 (4):
sqrt(5*sqrt(2)−1)/2
≈1.23197684757724599498
Edge 4 (3):
2*sqrt(sqrt(2)−1)
≈1.28718850581116524947
Edge 5 (2):
sqrt(1+sqrt(2))
≈1.5537739740300373073
Edge 6 (4):
2*sqrt(2*(sqrt(2)−1))
≈1.8203594422489093652
Edge-scribed Radius:
1
Volume:
2*(10*sqrt(2)−9)/3
≈3.4280904158206336587