Catalan Solids

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Tetrakis Hexahedron
canonical form
Vertices:  14  (6[4] + 8[6])
Faces:24  (isosceles triangles)
Edges:36  (24 short + 12 long)
Symmetry:  Full Octahedral  (Oh)
Dihedral Angle:  acos(−4/5)    ≈143.130102354 degrees
Dual Solid:  Truncated Octahedron
(values below based on unit-edge-length Truncated Octahedron)
Short Edge (24):  9*sqrt(2)/8    ≈1.5909902576697319299
Long Edge (12):  3*sqrt(2)/2    ≈2.1213203435596425732
[4]-Vertex Radius (6):  9*sqrt(2)/8    ≈1.5909902576697319299
[6]-Vertex Radius (8):  3*sqrt(6)/4    ≈1.8371173070873835736
Edge-scribed Radius:  3/2    1.5
Inscribed Radius:  9*sqrt(10)/20    ≈1.4230249470757706994
Volume:81*sqrt(2)/8    ≈14.318912319027587369


References:[1]Eugène Catalan, Mémoire sur la Théorie des Polyèdres,
Journal de l'École polytechnique 41 (1865), 1-71, +7 plates.