Self-Intersecting Truncated Regular Polyhedra

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

(Uniform #58) Small Stellated Truncated Dodecahedron
Vertices:  60  (60[3])
Faces:24  (12 regular pentagons + 12 regular decagrams)
Edges:90
Symmetry:  Full Icosahedral  (Ih)
Decagram-Pentagon Angle:  acos(sqrt(5)/5)    ≈63.434948823 degrees
Decagram-Decagram Angle:  acos(−sqrt(5)/5)    ≈116.565051177 degrees
Dual Solid:  Great Pentakis Dodecahedron
(values below based on edge length = 1)
Circumscribed Radius:  sqrt(2*(17−5*sqrt(5)))/4    ≈0.85291119940040149513
Midscribed Radius:  (5−sqrt(5))/4    ≈0.69098300562505257590
Pentagon Center Radius:  sqrt(10*(65−29*sqrt(5)))/20    ≈0.062054140173339523143
Decagram Center Radius:  sqrt(2*(5−sqrt(5)))/4    ≈0.58778525229247312917


References:[1]Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172.
[2]Johann Pitsch, Über Halbreguläre Sternpolyeder,
Zeitschrift für das Realschulwesen 6 (1881), 9-24, 64-65, 72-89, 216.