Derived Solids

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Expanded Icosidodecahedron (canonical)
canonical form
Vertices:  120  (60[4] + 60[4])
Faces:122  (20 equilateral triangles + 30 rhombi
    + 60 isosceles trapezoids + 12 regular pentagons)
Edges:240  (60 short + 120 medium + 60 long)
Symmetry:  Full Icosahedral  (Ih)
(values below based on edge-scribed radius = 1)
Short Edge (60):  sqrt(root[8th-order polynomial])    ≈0.27241701306694035114
Medium Edge (120):  sqrt(root[8th-order polynomial])    ≈0.32004918707655361359
Long Edge (60):  sqrt(root[8th-order polynomial])    ≈0.36768136108616687603
Rhombus Length:  sqrt(root[8th-order polynomial])    ≈0.48513115900512612294
Rhombus Width:  sqrt(root[8th-order polynomial])    ≈0.41758075525075899434549
Rhombus Angle:  acos(root[8th-order polynomial])    ≈81.441005704 degrees
Edge-scribed Radius:  1
Volume:root[8th-order polynomial]    ≈4.1140856926666643344