Greater Self-Dual Solids

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Self-Dual Icosioctahedron #1 (canonical)
Vertices:  28  (12[3] + 12[4] + 4[6])
Faces:28  (12 acute triangles + 12 irregular tetragons + 4 triambi)
Edges:54  (4 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
(values below based on edge-scribed radius = 1)
Edge 1 (24):  sqrt(root[6th-order polynomial])    ≈0.58028172222769431277
Edge 2 (12):  sqrt(root[6th-order polynomial])    ≈0.75675388860918686226
Edge 3 (6):  sqrt(root[6th-order polynomial])    ≈0.76843025043627703802
Edge 4 (12):  sqrt(root[6th-order polynomial])    ≈0.94490241681776958751
Max Vertex Radius:  sqrt(root[6th-order polynomial])    ≈1.1464598723729189991
Edge-scribed Radius:  1
Volume:root[6th-order polynomial]    ≈3.8943317273577077758