Higher Genus Toroidal Solids

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

Regular Map {4,6}10 (Schulte & Wills)
Vertices:  20  (4[6] + 4[6] + 12[6])
Faces:30  ({12 + 6} rectangles + 12 isosceles trapezoids)
Edges:60  (5 different lengths)
Symmetry:  Full Tetrahedral  (Td)
Dual Toroid:  Regular Map {6,4}10
(values below based on integer coordinates)
Edge 1 (18):  2*sqrt(2)    ≈2.8284271247461900976
Edge 2 (12):  sqrt(43)    ≈6.5574385243020006523
Edge 3 (12):  5*sqrt(3)    ≈8.6602540378443864676
Edge 4 (12):  10*sqrt(2)    ≈14.142135623730950488
Edge 5 (6):  18*sqrt(2)    ≈25.455844122715710878
Volume:608  [EXACT]


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