Regular Higher Genus Toroids

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Klein Map {7,3}_8 (minimal rational coordinates)
version 5
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 rational coordinates)
Edge 1 (12):  37/84    ≈0.44047619047619047619
Edge 2 (12):  3*sqrt(1033)/140    ≈0.68872108628520845588
Edge 3 (12):  4*sqrt(2)/7    ≈0.80812203564176859932
Edge 4 (12):  sqrt(67)/10    ≈0.81853527718724499700
Edge 5 (12):  sqrt(1033)/20    ≈1.6070158679988197304
Edge 6 (12):  215/84    ≈2.5595238095238095238
Edge 7 (12):  5*sqrt(57)/12    ≈3.14576434802947904052
Volume:27481/1470    ≈18.694557823129251701


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