Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with C4 Symmetry
(2 of 5)
Vertices:  14  (4[3] + 4[3] + 4[4] + 1[4] + 1[4])
Faces:12  (4 acute triangles + 4 kites + 4 irregular pentagons)
Edges:24  (5 different lengths)
Symmetry:  4-fold Cyclic  (C4)
Dual Solid:  Simplest C4 (1 of 5)
(values below based on edge-scribed radius = 1)
Edge 1 (4):  sqrt(root[16th-order polynomial])    ≈0.53421042986744935540
Edge 2 (8):  sqrt(root[16th-order polynomial])    ≈0.88458293867163668820
Edge 3 (4):  sqrt(root[16th-order polynomial])    ≈0.89791372512328824421
Edge 4 (4):  sqrt(root[16th-order polynomial])    ≈1.5239897890858199949
Edge 5 (4):  sqrt(root[16th-order polynomial])    ≈1.546525040833673344952
Edge-scribed Radius:  1
Volume:sqrt(root[16th-order polynomial])    ≈3.5333313414584961646