Self-Intersecting Truncated Regular Duals

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

Great Triakis Octahedron
Vertices:  14  (8[3] + 6[8])
Faces:24  (isosceles triangles)
Edges:36  (12 short + 24 long)
Symmetry:  Full Octahedral  (Oh)
Dihedral Angle:  acos((8*sqrt(2)−3)/17)    ≈60.722386810 degrees
Dual Solid:  Stellated Truncated Hexahedron
(values below based on unit-edge-length Stellated Truncated Hexahedron)
Short Edge (12):  2−sqrt(2)    ≈0.58578643762690495120
Long Edge (24):  2
[8]-Vertex Radius (6):  sqrt(2)−1    ≈0.41421356237309504880
[3]-Vertex Radius (8):  sqrt(3)    ≈1.73205080756887729353
Edge-scribed Radius:  (2−sqrt(2))/2    ≈0.29289321881345247560
Inscribed Radius:  sqrt(17*(23−16*sqrt(2)))/17    ≈0.14804272078783030621