Regular Hexagonal Toroidal Solids

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Regular Hexagonal Toroid with 15 faces (type A) (version 1)
Vertices:  30  (30[3])
Faces:15  (5 convex hexagons + 10 nonconvex hexagons)
Edges:45  (10 short + 30 medium + 5 long)
Symmetry:  5-fold Dihedral  (D5)
Short Edge (10):  3−sqrt(5)    ≈0.76393202250021030359
Medium Edge (30):  sqrt(5)−1    ≈1.2360679774997896964
Long Edge (5):  sqrt(4*(5−2*sqrt(5)))    ≈1.4530850560107217718
Volume:10*(2*sqrt(5)−3)/3    ≈4.9071198499985979761


References:[1]Lajos Szilassi, personal communication