Symmetric Canonical Self-Dual Octahedra

6 total:  2 

This is the only one with D2h symmetry

This is the only one with 3 edge lengths

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Self-Dual Octahedron #2 (canonical)
Vertices:  8  (4[3] + 4[4])
Faces:8  (4 isosceles triangles + 4 isosceles trapezoids)
Edges:14  (2 short + 8 medium + 4 long)
Symmetry:  2-fold Prismatic  (D2h)
Trapezoid-Trapezoid Angle:  acos(0)    90 degrees
Trapezoid-Triangle Angle:  acos(−sqrt(10)/10)    ≈108.434948823 degrees
Triangle-Triangle Angle:  acos(−3/5)    ≈126.869897646 degrees
(values below based on edge-scribed radius = 1)
Short Edge (2):  1
Medium Edge (8):  3/21.5
Long Edge (4):  2
[3]-Vertex Radius (4):  sqrt(5)/2    ≈1.1180339887498948482
[4]-Vertex Radius (4):  sqrt(2)    ≈1.4142135623730950488
Trapezoid Plane Radius:  sqrt(2)/2    ≈0.70710678118654752440
Triangle Plane Radius:  2*sqrt(5)/5    ≈0.89442719099991587856
Edge-scribed Radius:  1
Volume:10/3≈3.3333333333333333333