Other Solids

(box: x-ray)  (F: faces)  (slider: perspective)  (image: L=rotate R=zoom)  (M: metrics)
Please use a browser that supports "canvas"

Jessen's Orthogonal Icosahedron
Vertices:  12  (12[5])
Faces:20  (8 equilateral triangles + 12 isosceles triangles)
Edges:30  (24 short + 6 long)
Symmetry:  Pyritohedral  (Th)
Isosceles Apes Angle:  acos(−1/3)    ≈109.471220634 degrees
Convex Dihedral Angle:  acos(0)    90 degrees
Concave Dihedral Angle:  acos(0)    270 degrees
The dual has the same polyhedral graph as the Dodecahedron
(values below based on long edge length = 4)
Short Edge (24):  sqrt(6)    ≈2.4494897427831780982
Long Edge (6):  4
Circumscribed Radius:  sqrt(5)    ≈2.2360679774997896964
Volume:20


References:[1]Børge Jessen, Orthogonal Icosahedra,
Nordisk Matematisk Tidsskrift 15 (1967), 90-96.
[2]Michael Goldberg, Unstable Polyhedral Structures,
Mathematics Magazine 51(3) (May 1978), 165-170.