Greater Self-Dual Solids

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Self-Dual Tetracontahedron #4 (canonical)
Vertices:  40  (4[3] + 12[3] + 12[4] + 12[5])
Faces:40  (4 equilateral triangles + 12 isosceles triangles
    + 12 irregular tetragons + 12 irregular pentagons)
Edges:78  (6 different lengths)
Symmetry:  Chiral Tetrahedral  (T)
(values below based on edge-scribed radius = 1)
Edge 1 (12):  sqrt(root[12th-order polynomial])    ≈0.41701649777727538548
Edge 2 (12):  sqrt(root[12th-order polynomial])    ≈0.49565866906685583654
Edge 3 (12):  sqrt(root[12th-order polynomial])    ≈0.56709950665957222306
Edge 4 (6):  sqrt(root[12th-order polynomial])    ≈0.59055970678211678790
Edge 5 (24):  sqrt(root[12th-order polynomial])    ≈0.66200054437483317441
Edge 6 (12):  sqrt(root[12th-order polynomial])    ≈0.73344138196754956093
Max Vertex Radius:  sqrt(root[12th-order polynomial])    ≈1.0651216199080822496
Edge-scribed Radius:  1
Volume:root[12th-order polynomial]    ≈4.0081735461591424786