Regular Triangular Toroidal Solids
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Anti-Hexagonal Iris Toroid
D6 antiprismatic form
Vertices:
12 (12[6])
Faces:
24 (12 equilateral triangles + 12 obtuse triangles)
Edges:
36 (24 short + 6 medium + 6 long)
Symmetry:
6-fold Dihedral (D6)
Dihedral Angle 1 (6):
acos((3+2*sqrt(3))/9)
≈44.091172088 degrees
Dihedral Angle 2 (12):
acos(sqrt(3*(2*sqrt(3)−3))/3)
≈66.838768774 degrees
Dihedral Angle 3 (12):
acos(−(2*sqrt(3)−1)/3)
≈145.221891332 degrees
Dihedral Angle 4 (6):
acos(5*sqrt(3)/9)
≈344.206830952 degrees
(values below based on short edge length = 1)
Short Edge (24):
1
Medium Edge (6):
sqrt(1+sqrt(3))
≈1.6528916502810694801
Long Edge (6):
sqrt(1+2*sqrt(3))
≈2.1128420705622449781
Volume:
3*sqrt(sqrt(3)−1)/2
≈1.283399515751028289454