Non-Regular Toroidal Solids

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Isohedral Toroid with 32 faces
Vertices:  16  (8[5] + 8[7])
Faces:32  (isosceles triangles)
Edges:48  (16 short + 32 long)
Symmetry:  4-fold Antiprismatic  (D4v)
(values below based on short edge length = 1)
Short Edge (16):  1
Long Edge (32):  sqrt(1+2*sqrt(2)+2*sqrt(2−sqrt(2)))/2    ≈1.1574930727877542232
[5]-Vertex Radius (8):  sqrt(13+4*sqrt(2)+2*sqrt(34+23*sqrt(2)))/4    ≈1.4783787678385512316
[7]-Vertex Radius (8):  sqrt(5+4*sqrt(2)+2*sqrt(2−sqrt(2)))/4    ≈0.87276815288170672637
Volume:4*sqrt(2*sqrt(2)−1+2*sqrt(2−sqrt(2)))/3    ≈2.4437351572110715886


References:[1]Is there a simpler single polygon toroid? (Ed Pegg)