Greater Self-Dual Solids

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Self-Dual Tetracontahedron #3 (canonical)
Vertices:  40  (4[3] + 12[3] + 12[3] + 12[6])
Faces:40  (4 equilateral triangles + 12 isosceles triangles
    + 12 acute triangles + 12 irregular hexagons)
Edges:78  (5 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
(values below based on edge-scribed radius = 1)
Edge 1 (12):  sqrt(root[9th-order polynomial])    ≈0.24438787544572138523
Edge 2 (12):  sqrt(root[9th-order polynomial])    ≈0.43182256944903480007
Edge 3 (24):  sqrt(root[9th-order polynomial])    ≈0.572763380274838876447
Edge 4 (12):  sqrt(root[9th-order polynomial])    ≈0.62165281351597278086
Edge 5 (18):  sqrt(root[9th-order polynomial])    ≈0.95002831834509027207
Max Vertex Radius:  sqrt(root[9th-order polynomial])    ≈1.10708556643757218049
Edge-scribed Radius:  1
Volume:root[9th-order polynomial]    ≈3.9024645601850868862