Greater Self-Dual Solids

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Self-Dual Tetracontahedron #1 (canonical)
Vertices:  40  (12[3] + 12[3] + 12[4] + 4[9])
Faces:40  (12 acute triangles + 12 obtuse triangles
    + 12 irregular tetragons + 4 irregular enneagons)
Edges:78  (7 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
(values below based on edge-scribed radius = 1)
Edge 1 (12):  sqrt(root[10th-order polynomial])    ≈0.254445319059012435046
Edge 2 (12):  sqrt(root[10th-order polynomial])    ≈0.45306209179913303447
Edge 3 (12):  sqrt(root[10th-order polynomial])    ≈0.49456692196665572147
Edge 4 (6):  sqrt(root[10th-order polynomial])    ≈0.69318369470677632089
Edge 5 (12):  sqrt(root[10th-order polynomial])    ≈0.7338309616489243092549
Edge 6 (12):  sqrt(root[10th-order polynomial])    ≈0.77533579181644699626
Edge 7 (12):  sqrt(root[10th-order polynomial])    ≈0.97395256455656759568
Max Vertex Radius:  sqrt(root[10th-order polynomial])    ≈1.1805005165139436233
Edge-scribed Radius:  1
Volume:root[10th-order polynomial]    ≈3.8970014888705124743