Regular Tetragonal Toroidal Solids

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)
Please use a browser that supports "canvas"

Regular Tetragonal Toroid with 9 faces
Vertices:  9  (3[4] + 6[4])
Faces:9  (3 squares + 6 tri-equilateral trapezoids)
Edges:18
Symmetry:  3-fold Prismatic  (D3h)
(This toroid derived from a Triangular Dipyramid and a Triangular Prism)
Dihedral Angle 1 (6):  acos(2*sqrt(7)/7)    ≈40.893394649 degrees
Dihedral Angle 2 (9):  acos(−1/7)    ≈98.213210702 degrees
Dihedral Angle 3 (3):  acos(1/2)    300 degrees
Dual Toroid:  Regular Tetragonal Toroid with 9 faces (itself)
(values below based on short edge length = 2)
Short Edge (15):  2
Long Edge (3):  5
Inner Vertex Radius (6):  sqrt(21)/3    ≈1.5275252316519466689
Outer Vertex Radius (3):  5*sqrt(3)/3    ≈2.886751345948128822546
Volume:9*sqrt(3)/2    ≈7.7942286340599478209


References:[1]On Some Regular Toroids (Lajos Szilassi)
[2]Lajos Szilassi, On Three Classes of Regular Toroids,
3rd International Conference APLIMAT 2004.