Regular Higher Genus Toroids

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Klein Map {7,3}_8 (rational coordinates)
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 rational coordinates)
Edge 1 (12):  sqrt(100653175429/161790581824)    ≈0.78874591305631403609
Edge 2 (12):  sqrt(66844487762245/29686980427776)    ≈1.5005476350889218939
Edge 3 (12):  sqrt(16225105/4848804)    ≈1.8292642351863649400
Edge 4 (6):  sqrt(1047625/300304)    ≈1.8677655824769071456
Edge 5 (6):  sqrt(1244485/200704)    ≈2.4901001770813378672
Edge 6 (12):  sqrt(87392016681385/9961210805058)    ≈2.9619642688679887700
Edge 7 (12):  sqrt(4194026028637/135612481536)    ≈5.5611643388655426858
Edge 8 (12):  sqrt(1338524265625/42747216516)    ≈5.59576160325780924048
Volume:1884700317774305/12224972014416    ≈154.16806807834145801


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)