Non-Regular Toroidal Solids

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Octagonal Iris Toroid
Vertices:  16  (16[5])
Faces:24  (8 squares + 16 obtuse triangles)
Edges:40  (24 short + 8 medium + 8 long)
Symmetry:  8-fold Dihedral  (D8)
Dihedral Angle 1 (8):  acos((7+4*sqrt(2))/17)    ≈41.882040944 degrees
Dihedral Angle 2 (16):  acos(sqrt(34*(5−2*sqrt(2)))/17)    ≈59.6388065952 degrees
Dihedral Angle 3 (8):  acos(−sqrt(2)/2)    135 degrees
Dihedral Angle 4 (8):  acos((3+9*sqrt(2))/17)    ≈337.694288208 degrees
(values below based on short edge length = 1)
Short Edge (24):  1
Medium Edge (8):  sqrt(3+sqrt(2))    ≈2.1010029896154586502
Long Edge (8):  sqrt(2*(2+sqrt(2)))    ≈2.6131259297527530557
Volume:2*(2+sqrt(2))/3    ≈2.2761423749153966992