Symmetric Canonical Self-Dual Decahedra
28 total:
5
3 have C3v symmetry:
3
5 have 6 edge lengths:
1
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(F: faces)
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Self-Dual Decahedron #5 (canonical)
Vertices:
10 (1[3] + 3[3] + 3[4] + 3[4])
Faces:
10 (1 equilateral triangle + 3 isosceles triangles
+ {3 * 2} isosceles trapezoids)
Edges:
18 (6 different lengths)
Symmetry:
3-fold Pyramidal (C3v)
(Each large trapezoid is a 120-60 isosceles trapezoid)
(values below based on edge-scribed radius = 1)
Edge 1 (3):
2*sqrt(2)/11
≈0.25712973861329000887
Edge 2 (3):
22*sqrt(2)/57
≈0.54583681354751036971
Edge 3 (3):
2*sqrt(2)/3
≈0.94280904158206336587
Edge 4 (3):
12*sqrt(2)/11
≈1.5427784316797400532
Edge 5 (3):
4*sqrt(2)/3
≈1.8856180831641267317
Edge 6 (3):
2*sqrt(2)
≈2.8284271247461900976
Edge-scribed Radius:
1
Volume:
706936/227601
≈3.1060320473108641878