Catalan Solids

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Triakis Tetrahedron
Vertices:  8  (4[3] + 4[6])
Faces:12  (isosceles triangles)
Edges:18  (12 short + 6 long)
Symmetry:  Full Tetrahedral  (Td)
Dihedral Angle:  acos(−7/11)    ≈129.521196359 degrees
Dual Solid:  Truncated Tetrahedron
(values below based on unit-edge-length Truncated Tetrahedron)
Short Edge (12):  9/5    1.8
Long Edge (6):  3
[3]-Vertex Radius (4):  9*sqrt(6)/20    ≈1.1022703842524301442
[6]-Vertex Radius (4):  3*sqrt(6)/4    ≈1.8371173070873835736
Edge-scribed Radius:  3*sqrt(2)/4    ≈1.0606601717798212866
Inscribed Radius:  9*sqrt(22)/44    ≈0.95940322360024695434
Volume:81*sqrt(2)/20    ≈5.7275649276110349476


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