Catalan Solids

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Deltoidal Icositetrahedron
Vertices:  26  (8[3] + 6[4] + 12[4])
Faces:24  (tri-equiangular kites)
Edges:48  (24 short + 24 long)
Symmetry:  Full Octahedral  (Oh)
Dihedral Angle:  acos(−(7+4*sqrt(2))/17)    ≈138.117959056 degrees
Dual Solid:  Rhombicuboctahedron
(values below based on unit-edge-length Rhombicuboctahedron)
Short Edge (24):  2*sqrt(10−sqrt(2))/7    ≈0.83718607580427642316
Long Edge (24):  sqrt(2*(2−sqrt(2)))    ≈1.0823922002923939688
Kite Length:  2*sqrt(31−8*sqrt(2))/7    ≈1.2676924722362712507
Kite Width:  sqrt(2)    ≈1.4142135623730950488
[3]-Vertex Radius (8):  (4*sqrt(3)+sqrt(6))/7    ≈1.3396704247226696103
[4]-Vertex Radius (18):  sqrt(2)    ≈1.4142135623730950488
Edge-scribed Radius:  sqrt(2*(2+sqrt(2)))/2    ≈1.3065629648763765279
Inscribed Radius:  sqrt(34*(7+4*sqrt(2)))/17    ≈1.2202629537976100741
Volume:16*(1+2*sqrt(2))/7    ≈8.7506905708484345088


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