Higher Genus Toroidal Solids

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Klein Map {7,3}8 (minimal integer coordinates)
version 2
Vertices:  56  (4[3] + 4[3] + 12[3] + 12[3] + 12[3] + 12[3])
Faces:24  ({12 * 2} nonconvex heptagons)
Edges:84  (7 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
Dual Toroid:  Klein Map Dual {3,7}8
(values below based on minimal integer coordinates)
Edge 1 (12):  sqrt(29)    ≈5.3851648071345040313
Edge 2 (12):  11*sqrt(11)    ≈36.482872693909398340
Edge 3 (12):  7*sqrt(53)    ≈50.960769224963627898
Edge 4 (12):  42*sqrt(2)    ≈59.3969696196699920497
Edge 5 (12):  13*sqrt(29)    ≈70.007142492748552406
Edge 6 (12):  49*sqrt(5)    ≈109.56733089748969512
Edge 7 (12):  21*sqrt(65)    ≈169.30741271426954270
Volume:1802416  [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)