Regular Hexagonal Toroidal Solids

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Regular Hexagonal Toroid with 9 faces (type A) (cubic form)
cubic form
Vertices:  18  (18[3])
Faces:9  (3 convex hexagons + 6 nonconvex hexagons)
Edges:27  (4 different lengths)
Symmetry:  3-fold Dihedral  (D3)
Dihedral Angle 1 (6):  acos(sqrt(2)/2)    45 degrees
Dihedral Angle 2 (18):  acos(0)    90 degrees
Dihedral Angle 3 (3):  acos(1/2)    300 degrees
Dual Toroid:  Regular Triangular Toroid with 18 faces (type A)
(values below based on long edge length = 6)
Edge 1 (6):  2*sqrt(2)    ≈2.8284271247461900976
Edge 2 (3):  2*sqrt(3)    ≈3.4641016151377545871
Edge 3 (12):  4
Edge 4 (6):  6
Volume:140  [EXACT]


References:[1]On Some Regular Toroids (Lajos Szilassi)
[2]Lajos Szilassi, On Three Classes of Regular Toroids,
3rd International Conference APLIMAT 2004.