Biscribed Non-Chiral Solids

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Biscribed Disdyakis Dodecahedron
biscribed form
Vertices:  26  (12[4] + 8[6] + 6[8])
Faces:48  (acute triangles)
Edges:72  (24 short + 24 medium + 24 long)
Symmetry:  Full Octahedral  (Oh)
Short Edge Angle:  acos(−(539+600*sqrt(2)    
    +176*sqrt(3)−204*sqrt(6))/1633)    
≈136.916340788 degrees
Medium Edge Angle:  acos(−(343−212*sqrt(2)    
    +112*sqrt(3)+464*sqrt(6))/1633)    
≈147.270951511 degrees
Long Edge Angle:  acos(−(149+384*sqrt(2)    
    −18*sqrt(3)+392*sqrt(6))/1633)    
≈173.073280013 degrees
Dual Solid:  Biscribed Truncated Cuboctahedron
(values below based on circumscribed radius = 1)
Short Edge (24):  sqrt(6*(3−sqrt(6)))/3    ≈0.60581089305537246549
Medium Edge (24):  sqrt(2−sqrt(2))    ≈0.76536686473017954346
Long Edge (24):  sqrt(6*(3−sqrt(3)))/3    ≈0.91940168676196612196
Circumscribed Radius:  1
Inscribed Radius:  1/sqrt(9−2*sqrt(2)−2*sqrt(6))    ≈0.88645188628289125669
Volume:4*sqrt(6)/3    ≈3.2659863237109041309