Other Solids

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Schönhardt Polyhedron
Vertices:  6  (6[4])
Faces:8  (2 equilateral triangles + 6 isosceles triangles)
Edges:12  (9 short + 3 long)
Symmetry:  3-fold Dihedral  (D3)
(This version uses a twist angle of 30 degrees)
Short Edge (9):  sqrt(3)    ≈1.73205080756887729353
Long Edge (3):  sqrt(3+2*sqrt(3))    ≈2.5424597568374124783
Radius:  sqrt(5+sqrt(3))/2    ≈1.2973097941094175380
Volume:sqrt(3*(1+sqrt(3)))/2    ≈1.4314461588465903492


References:[1]Erich Schönhardt, Über Die Zerlegung Von Dreieckspolyedern
in Tetraeder, Mathematische Annalen 98 (1928), 309-312.
[2]Three Untetrahedralizable Objects