Simplest Canonical Polyhedra of Each Symmetry Type

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Simplest Canonical Polyhedron with D2 Symmetry
Vertices:  10  (4[3] + 4[4] + 2[4])
Faces:10  (4 acute triangles + 4 irregular tetragons + 2 rhombi)
Edges:18  (4 different lengths)
Symmetry:  2-fold Dihedral  (D2)
Dual Solid:  Simplest D2 (itself)
(values below based on edge-scribed radius = 1)
Edge 1 (4):  sqrt(3*(4−cbrt(26*(3*sqrt(78)−26))    
    +cbrt(26*(3*sqrt(78)+26))))/6    
≈1.0307209743835805352
Edge 2 (8):  sqrt(6*(cbrt(2*(3686−411*sqrt(78)))    
    +cbrt(2*(3686+411*sqrt(78)))−20))/6    
≈1.2438570593497324116
Edge 3 (4):  sqrt(3*(20+cbrt(2*(58−3*sqrt(78)))    
    +cbrt(2*(58+3*sqrt(78)))))/6    
≈1.5681179738050099551
Edge 4 (2):  2*sqrt(3*(2−cbrt(2*(3*sqrt(78)−4))    
    +cbrt(2*(3*sqrt(78)+4))))/3    
≈1.78125405877116183153
Edge-scribed Radius:  1
Volume:4*(18+cbrt(6*(23*sqrt(78)−198))    
    −cbrt(6*(23*sqrt(78)+198)))/9    
≈3.4367880932990821662