[size=50] [color=#ff0000][url=http://dmccooey.com/polyhedra/BiscribedPentakisDodecahedron.html ] Biscribed Pentakis Dodecahedron[/url][/color][br][b][u]Vertices[/u][/b]: 32 [b]([/b][color=#0000ff][b]12[5] + 20[6][/b][/color][b])[/b]; [u] [b]Faces[/b][/u]: 60 (isosceles triangles); [b][u]Edges[/u][/b]: 90 (60 short + 30 long)[br]Symmetry: Full Icosahedral (Ih)[br]Short Edge Angle: acos(−(255*sqrt(5)−7 [br] +sqrt(6*(5105+2099*sqrt(5))))/898) ≈153.789590509 degrees[br]Long Edge Angle: acos(−(560−195*sqrt(5) [br] +12*sqrt(15*(1205+298*sqrt(5))))/2245) ≈161.946011928 degrees[br][b]Dual Solid:[/b] [color=#1e84cc][url=http://dmccooey.com/polyhedra/BiscribedTruncatedIcosahedron.html]Biscribed Truncated Icosahedron[/url][/color][br](values below based on circumscribed radius = 1)[br][b]Short Edge (60)[/b]: sqrt(30*(15−sqrt(15*(5+2*sqrt(5)))))/15 ≈0.64085182017098754129[br][b]Long Edge (30)[/b]: (sqrt(15)−sqrt(3))/3 ≈0.71364417954617986388 [br] [b]Long Edge[/b] (30)/[b]Short Edge[/b] (60)= [b]1.113586880904497 [/b][br]Circumscribed Radius: 1[br]Inscribed Radius: 1/sqrt(10−sqrt(5)−sqrt(6*(5+sqrt(5)))) ≈0.92260219454398946762[br]Volume: 2*sqrt(10*(5−sqrt(5)))/3 ≈3.5048740807942240402[/size]