Higher Genus Toroidal Solids
(box: x-ray)
(F: faces)
(slider: perspective)
(image: L=rotate R=zoom)
(M: metrics)
Please use a browser that supports "canvas"
Klein Map Dual {3,7}
8
(Schulte & Wills)
Vertices:
24 (12[7] + 12[7])
Faces:
56 ({4 * 2} equilateral triangles + {12 * 4} obtuse triangles)
Edges:
84 (7 different lengths)
Symmetry:
Chiral Tetrahedral (T)
Dual Toroid:
Klein Map {7,3}
8
(values below based on integer coordinates)
Edge 1 (12):
sqrt(2)
≈1.4142135623730950488
Edge 2 (24):
sqrt(6)
≈2.4494897427831780982
Edge 3 (6):
10
Edge 4 (12):
sqrt(134)
≈11.575836902790225474
Edge 5 (12):
sqrt(146)
≈12.083045973594572068
Edge 6 (12):
5*sqrt(6)
≈12.247448713915890491
Edge 7 (6):
2*sqrt(41)
≈12.806248474865697373
Volume:
332/3
≈110.66666666666666667
References:
[1]
Egon Schulte and Jörg M. Wills, A polyhedral realization of
Felix Klein's Map {3,7}
8
on a Riemann surface of genus 3,
Journal of the London Mathematical Society
32
(1985), 539-547.