Regular Hexagonal Toroidal Solids

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Regular Hexagonal Toroid with 9 faces (type B)
Vertices:  18  (18[3])
Faces:9  ({6 + 3} nonconvex hexagons)
Edges:27  (6 different lengths)
Symmetry:  3-fold Dihedral  (D3)
Dual Toroid:  Regular Triangular Toroid with 18 faces (type B)
Edge 1 (3):  2*sqrt(19)    ≈8.71779788708134710447
Edge 2 (6):  sqrt(91)    ≈9.53939201416945649153
Edge 3 (6):  3*sqrt(19)    ≈13.076696830622020657
Edge 4 (3):  18*sqrt(3)    ≈31.176914536239791283
Edge 5 (3):  10*sqrt(11)    ≈33.166247903553998491
Edge 6 (6):  15*sqrt(11)    ≈49.749371855330997737
Volume:17664  [EXACT]


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