Versi-Regular Polyhedra

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

(Uniform #51) Small Dodecahemidodecahedron
Vertices:  30  (30[4])
Faces:18  (12 regular pentagons + 6 regular decagons)
Edges:60
Symmetry:  Full Icosahedral  (Ih)
Dihedral Angle:  acos(sqrt(5)/5)    ≈63.434948823 degrees
Dual Solid:  Small Dodecahemidodecacron
(values below based on edge length = 1)
Circumscribed Radius:  (1+sqrt(5))/2    ≈1.6180339887498948482
Midscribed Radius:  sqrt((5+2*sqrt(5))/4)    ≈1.5388417685876267013
Decagon Center Radius:  0
Pentagon Center Radius:  sqrt(5*(5+2*sqrt(5)))/5    ≈1.3763819204711735382


References:[1]Jean Paul Albert Badoureau, Mémoire sur les Figures Isocèles,
Journal de l'École polytechnique 49 (1881), 47-172.