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