{6,3} Genus-1 Toroids

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

Regular Hexagonal Toroid with 10 faces (version 3)
version 3
Vertices:  20  (20[3])
Faces:10  ({4 + 4 + 2} nonconvex hexagons)
Edges:30  (9 different lengths)
Symmetry:  2-fold Dihedral  (D2)
Dual Toroid:  Regular Triangular Toroid with 20 faces
(values below based on integer coordinates)
Edge 1 (4):  3*sqrt(2)    ≈4.2426406871192851464
Edge 2 (4):  4*sqrt(22)    ≈18.761663039293718218
Edge 3 (2):  24
Edge 4 (4):  18*sqrt(2)    ≈25.455844122715710878
Edge 5 (2):  12*sqrt(10)    ≈37.947331922020551984
Edge 6 (4):  15*sqrt(10)    ≈47.434164902525689980
Edge 7 (4):  14*sqrt(22)    ≈65.665820637528013764
Edge 8 (4):  15*sqrt(34)    ≈87.464278422679507063
Edge 9 (2):  96*sqrt(2)    ≈135.76450198781712468
Volume:53856  [EXACT]


References:[1]Lajos Szilassi, Locally regular toroids with hexagonal faces,
Symmetry: Culture and Science 20(1-4) (2009), 269-295.