Regular Hexagonal Toroidal Solids

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Regular Hexagonal Toroid with 12 faces (type A) (trapezohedral form)
trapezohedral form
Vertices:  24  (24[3])
Faces:12  (4 convex hexagons + 8 nonconvex hexagons)
Edges:36  (5 different lengths)
Symmetry:  4-fold Dihedral  (D4)
Dual Toroid:  Regular Triangular Toroid with 24 faces
Edge 1 (8):  2*sqrt(5)    ≈4.4721359549995793928
Edge 2 (12):  4*sqrt(2)    ≈5.6568542494923801952
Edge 3 (8):  sqrt(35)    ≈5.9160797830996160426
Edge 4 (4):  6
Edge 5 (4):  4*sqrt(3)    ≈6.9282032302755091741
Volume:368  [EXACT]


References:[1]Lajos Szilassi, Locally regular toroids with hexagonal faces,
Symmetry: Culture and Science 20(1-4) (2009), 269-295.