Higher Genus Toroidal Solids

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Hendecagonal Dodecahedron with 12 overarching faces
Vertices:  44  ({(2 * 2) * 11}[3])
Faces:12  ({(2 * 2) * 3} nonconvex hendecagons)
Edges:66 (16 different lengths)
Symmetry:  2-fold Rotoreflection  (S4)
(values below based on integer coordinates)
Edge 1 (4):  2
Edge 2 (4):  14
Edge 3 (4):  4*sqrt(17)    ≈16.492422502470642199
Edge 4 (8):  4*sqrt(22)    ≈18.761663039293718218
Edge 5 (4):  12*sqrt(3)    ≈20.784609690826527522
Edge 6 (4):  9*sqrt(6)    ≈22.045407685048602884
Edge 7 (4):  24
Edge 8 (4):  24*sqrt(2)    ≈33.941125496954281171
Edge 9 (2):  36
Edge 10 (4):  15*sqrt(6)    ≈36.742346141747671473
Edge 11 (8):  6*sqrt(38)    ≈36.986484017813858702
Edge 12 (4):  12*sqrt(14)    ≈44.899888641287296627
Edge 13 (4):  36*sqrt(2)    ≈50.911688245431421757
Edge 14 (2):  60
Edge 15 (4):  57*sqrt(2)    ≈80.610173055266417782
Edge 16 (2):  96*sqrt(2)    ≈135.76450198781712468
Volume:259472  [EXACT]
Planes
Red: x + y + z + 48 = 0
x + y - z - 48 = 0
x - y + z - 48 = 0
x - y - z + 48 = 0
Blue: 3x + 2z - 60 = 0
3x - 2z + 60 = 0
3y + 2z + 60 = 0
3y - 2z - 60 = 0
Green: x + z - 18 = 0
x - z + 18 = 0
y + z + 18 = 0
y - z - 18 = 0


References:[1]Minimal surfaces for planar octagons and nonagons (Ivan Neretin)