Symmetric Canonical Self-Dual Decahedra

28 total:  12 

10 have C2 symmetry:  1 

5 have 6 edge lengths:  4 

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

Self-Dual Decahedron #12 (canonical)
Vertices:  10  (2[3] + 2[3] + 2[4] + 4[4])
Faces:10  ({2 * 2} isosceles triangles + 2 isosceles trapezoids
    + 4 irregular tetragons)
Edges:18  (6 different lengths)
Symmetry:  2-fold Cyclic  (C2)
(values below based on edge-scribed radius = 1)
Edge 1 (1):  sqrt(sqrt(2)−1)    ≈0.64359425290558262474
Edge 2 (4):  sqrt(17*sqrt(2)−23)    ≈1.0206030375922931916
Edge 3 (4):  sqrt(5*sqrt(2)−1)/2    ≈1.23197684757724599498
Edge 4 (3):  2*sqrt(sqrt(2)−1)    ≈1.28718850581116524947
Edge 5 (2):  sqrt(1+sqrt(2))    ≈1.5537739740300373073
Edge 6 (4):  2*sqrt(2*(sqrt(2)−1))    ≈1.8203594422489093652
Edge-scribed Radius:  1
Volume:2*(10*sqrt(2)−9)/3    ≈3.4280904158206336587