Higher Genus Toroidal Solids

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

Regular Map {6,4}10 (Schulte & Wills)
Vertices:  30  (12[4] + 12[4] + 6[4])
Faces:20  ({4 * 2} regular hexagons + 12 mirror-symmetric hexagons)
Edges:60  (4 different lengths)
Symmetry:  Full Tetrahedral  (Td)
Dual Toroid:  Regular Map {4,6}10
(values below based on integer coordinates)
Edge 1 (18):  2*sqrt(2)    ≈2.8284271247461900976
Edge 2 (12):  sqrt(11)    ≈3.3166247903553998491
Edge 3 (12):  3*sqrt(3)    ≈5.1961524227066318806
Edge 4 (18):  6*sqrt(2)    ≈8.4852813742385702928
Volume:816  [EXACT]


References:[1]Egon Schulte and Jörg M. Wills, On Coxeter's regular skew
polyhedra, Discrete Mathematics 60 (1986), 253-262.