Regular Higher Genus Toroids

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

Klein Map {7,3}_8 (small integer coordinates)
version 4
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 small integer coordinates)
Edge 1 (12):  2*sqrt(633)    ≈50.318982501636497220
Edge 2 (12):  2*sqrt(777)    ≈55.749439459065415791
Edge 3 (6):  10*sqrt(41)    ≈64.0312423743284868649
Edge 4 (12):  5*sqrt(453)    ≈106.41898326896381319
Edge 5 (6):  76*sqrt(2)    ≈107.48023074035522371
Edge 6 (12):  9*sqrt(237)    ≈138.55323886506587183
Edge 7 (12):  39*sqrt(73)    ≈333.216146067383715547
Edge 8 (12):  50*sqrt(57)    ≈377.49172176353748486
Volume:29960400  [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)