Symmetric Canonical Self-Dual Decahedra

28 total:  6 

2 have C2v symmetry:  1 

5 have 6 edge lengths:  2 

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

Self-Dual Decahedron #6 (canonical)
Vertices:  10  (2[3] + 4[3] + 2[4] + 2[5])
Faces:10  (2 isosceles triangles + 4 acute triangles + 2 kites
    + 2 mirror-symmetric pentagons)
Edges:18  (6 different lengths)
Symmetry:  2-fold Pyramidal  (C2v)
(values below based on edge-scribed radius = 1)
Edge 1 (4):  (3*sqrt(10)−5*sqrt(2))/3    ≈0.80525505621322091733
Edge 2 (4):  2*(3*sqrt(10)−5*sqrt(2))/5    ≈0.96630606745586510080
Edge 3 (1):  2*sqrt(10)/5    ≈1.2649110640673517328
Edge 4 (4):  sqrt(10)−sqrt(2)    ≈1.7480640977952842832
Edge 5 (4):  4*sqrt(2)/3    ≈1.8856180831641267317
Edge 6 (1):  2*sqrt(2)    ≈2.8284271247461900976
Edge-scribed Radius:  1
Volume:8*(13*sqrt(5)−10)/45    ≈3.3900237702217361873