Non-Regular Toroidal Solids

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Hexagonal Trapezohedron Toroid
Vertices:  36  (12[3] + 12[3] + 12[4])
Faces:24  ({12 * 2} mirror-symmetric pentagons)
Edges:60  (5 different lengths)
Symmetry:  6-fold Antiprismatic  (D6v)
(values below based on long edge length = 1)
Edge 1 (12):  sqrt(6*(11*sqrt(3)−19))/2    ≈0.28078163203186091461
Edge 2 (12):  sqrt(3*sqrt(3)−5)    ≈0.44289098286895826186
Edge 3 (12):  sqrt(2*(sqrt(3)−1))/2    ≈0.60500033370605560912
Edge 4 (12):  sqrt(211*sqrt(3)−365)    ≈0.68023554525848539657
Edge 5 (12):  1
Volume:3*sqrt(2*(64889*sqrt(3)−112391))    ≈0.89852215544002844826