Symmetric Canonical Self-Dual Dodecahedra

91 total:  5 

2 have C2h symmetry:  1 

2 have 5 edge lengths:  2 

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)

Self-Dual Dodecahedron #5 (canonical)
Vertices:  12  (4[3] + 2[4] + 2[4] + 4[4])
Faces:12  (4 acute triangles + {2 * 2} kites + 4 irregular tetragons)
Edges:22  (5 different lengths)
Symmetry:  2-fold Cyclic + Perpendicular Reflection  (C2h)
(values below based on edge-scribed radius = 1)
Edge 1 (4):  sqrt(34−23*sqrt(2))/2    ≈0.60685419694907233079
Edge 2 (4):  sqrt(2*(26−17*sqrt(2)))/2    ≈0.98953762931416210251
Edge 3 (8):  3*sqrt(2−sqrt(2))/2    ≈1.1480502970952693152
Edge 4 (2):  2*sqrt(2−sqrt(2))    ≈1.5307337294603590869
Edge 5 (4):  sqrt(10+sqrt(2))/2    ≈1.6892463972414662996
Edge-scribed Radius:  1
Volume:4*(4−sqrt(2))/3    ≈3.4477152501692066016