Regular Hexagonal Toroidal Solids

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

Regular Hexagonal Toroid with 9 faces (type A) (triangular form)
triangular form
Vertices:  18  (18[3])
Faces:9  ({6 + 3} nonconvex hexagons)
Edges:27  (4 different lengths)
Symmetry:  3-fold Dihedral  (D3)
Dihedral Angle 1 (6):  acos(sqrt(2)/2)    45 degrees
Dihedral Angle 2 (3):  acos(1/2)    60 degrees
Dihedral Angle 3 (12):  acos(0)    90 degrees
Dihedral Angle 4 (6):  acos(0)    270 degrees
Dual Toroid:  Regular Triangular Toroid with 18 faces (type A)
(values below based on short edge length = 2)
Edge 1 (12):  2
Edge 2 (6):  4*sqrt(2)    ≈5.6568542494923801952
Edge 3 (6):  8
Edge 4 (3):  6*sqrt(3)    ≈10.392304845413263761
Volume:120  [EXACT]