Self-Dual Hexahedron #2 (canonical)

2 total:

2

This is the only one with C2 symmetry

This is the only one with 5 edge lengths

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

Self-Dual Hexahedron #2 (canonical)

Vertices:	6 (4[3] + 2[4])
Faces:	6 (2 isosceles triangles + 2 scalene triangles + 2 irregular tetragons)
Edges:	10 (5 different lengths)
Symmetry:	2-fold Cyclic (C2)
(values below based on edge-scribed radius = 1)
Edge 1 (2):	sqrt(2(2sqrt(2+sqrt(5))−1−sqrt(5)))	≈1.3268564934032578372
Edge 2 (1):	2sqrt(sqrt(2(5*sqrt(5)−11)))	≈1.5499241426618984256
Edge 3 (4):	sqrt(2(sqrt(2(29+13sqrt(5)))−4−2sqrt(5)))	≈2.1468989045199718192
Edge 4 (2):	sqrt(2(sqrt(2(sqrt(5)−1))−1+sqrt(5)))	≈2.3699665537786124076
Edge 5 (1):	2sqrt(sqrt(2(1+sqrt(5))))	≈3.1900089648953263896
Edge-scribed Radius:	1
Volume:	8*(1+sqrt(5)−sqrt(2+sqrt(5)))/3	≈3.1410585339421265229