Regular Higher Genus Toroids

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Klein Map {7,3}_8 (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  (8 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
Dual Toroid:  Klein Map Dual {3,7}_8
(values below based on integer coordinates)
Edge 1 (12):  8116335024*sqrt(204829)    ≈3673293986132.7369893
Edge 2 (12):  13268175589*sqrt(277405)    ≈6988248702956.2599507
Edge 3 (12):  99402912448*sqrt(7345)    ≈8519125364619.1997669
Edge 4 (6):  722365395360*sqrt(145)    ≈8698431228674.1291958
Edge 5 (6):  1257841508286*sqrt(85)    ≈11596725705871.116686
Edge 6 (12):  188944727104*sqrt(5330)    ≈13794259159851.928118
Edge 7 (12):  54847666661*sqrt(222973)    ≈25899077489599.815698
Edge 8 (12):  723615368000*sqrt(1297)    ≈26060201523493.457531
Volume:15572205552796989531635911248996860559360  [EXACT]


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)