Higher Genus Toroidal Solids

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Klein Map {7,3}8 (basic shape)
version 1
Vertices:  56  (4[3] + 4[3] + 12[3] + 12[3] + 12[3] + 12[3])
Faces:24  ({12 * 2} nonconvex heptagons)
Edges:84  (8 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
Dual Toroid:  Klein Map Dual {3,7}8
(values below based on integer coordinates)
Edge 1 (12):  34*sqrt(185)    ≈462.44999729700507373
Edge 2 (12):  69*sqrt(67)    ≈564.78934125919904793
Edge 3 (6):  418*sqrt(2)    ≈591.14126907195373040
Edge 4 (12):  57*sqrt(305)    ≈995.46220420465989684
Edge 5 (12):  99*sqrt(185)    ≈1346.5455803648088912
Edge 6 (6):  1026*sqrt(2)    ≈1450.9831149947955201
Edge 7 (12):  152*sqrt(281)    ≈2547.98430136451193952
Edge 8 (12):  399*sqrt(65)    ≈3216.8408415711213113
Volume:12635620920  [EXACT]


References:[1]Felix Klein, Über die Transformationen siebenter
Ordnung der elliptischen Funktionen,
Mathematische Annalen 14 (1879), 428-471.
[2]Felix Klein, translated by Silvio Levy,
On the Order-Seven Transformation of Elliptic Functions
[3]Klein's Quartic Curve (John Baez)
[4]Klein's Quartic Curve (Greg Egan)