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