Regular Hexagonal Toroidal Solids

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Regular Hexagonal Toroid with 11 faces
Vertices:  22  (22[3])
Faces:11  (2 convex hexagons + {2 * 4 + 1} nonconvex hexagons)
Edges:33  (12 different lengths)
Symmetry:  2-fold Cyclic  (C2)
Dual Toroid:  Regular Triangular Toroid with 22 faces
Edge 1 (2):  sqrt(2)    ≈1.4142135623730950488
Edge 2 (4):  2*sqrt(2)    ≈2.8284271247461900976
Edge 3 (2):  3
Edge 4 (1):  2*sqrt(3)    ≈3.4641016151377545871
Edge 5 (2):  4
Edge 6 (2):  5
Edge 7 (6):  6
Edge 8 (1):  4*sqrt(3)    ≈6.9282032302755091741
Edge 9 (2):  5*sqrt(2)    ≈7.0710678118654752440
Edge 10 (3):  8
Edge 11 (4):  5*sqrt(3)    ≈8.6602540378443864676
Edge 12 (4):  9
Volume:1411/3    ≈470.33333333333333333


References:[1]Lajos Szilassi, personal communication