Non-Regular Toroidal Solids
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Tetragonal Trapezohedron Toroid
Vertices:
24 (8[3] + 8[3] + 8[4])
Faces:
16 ({8 * 2} mirror-symmetric pentagons)
Edges:
40 (4 different lengths)
Symmetry:
4-fold Antiprismatic (D4v)
(values below based on long edge length = 1)
Edge 1 (16):
sqrt(5*sqrt(2)−7)
≈0.26658546821887205787
Edge 2 (8):
sqrt(sqrt(2)−1)
≈0.64359425290558262474
Edge 3 (8):
3*sqrt(5*sqrt(2)−7)
≈0.79975640465661617362
Edge 4 (8):
1
Volume:
2*sqrt(2*(1723*sqrt(2)−2436))/3
≈0.78313783026589420422