Biscribed Pentakis Dodecahedron: The Icosahedron-Dodecahedron Compound whose all vertices lie on the same sphere

Author:
Roman Chijner
Topic:
Algebra, Calculus, Circle, Difference and Slope, Differential Calculus, Differential Equation, Optimization Problems, Geometry, Function Graph, Intersection, Linear Programming or Linear Optimization, Mathematics, Sphere, Surface, Vectors
Biscribed Pentakis Dodecahedron Vertices: 32 (12[5] + 20[6]); Faces: 60 (isosceles triangles); Edges: 90 (60 short + 30 long) Symmetry: Full Icosahedral (Ih) Short Edge Angle: acos(−(255*sqrt(5)−7 +sqrt(6*(5105+2099*sqrt(5))))/898) ≈153.789590509 degrees Long Edge Angle: acos(−(560−195*sqrt(5) +12*sqrt(15*(1205+298*sqrt(5))))/2245) ≈161.946011928 degrees Dual Solid: Biscribed Truncated Icosahedron (values below based on circumscribed radius = 1) Short Edge (60): sqrt(30*(15−sqrt(15*(5+2*sqrt(5)))))/15 ≈0.64085182017098754129 Long Edge (30): (sqrt(15)−sqrt(3))/3 ≈0.71364417954617986388 Long Edge (30)/Short Edge (60)= 1.113586880904497 Circumscribed Radius: 1 Inscribed Radius: 1/sqrt(10−sqrt(5)−sqrt(6*(5+sqrt(5)))) ≈0.92260219454398946762 Volume: 2*sqrt(10*(5−sqrt(5)))/3 ≈3.5048740807942240402
Image

Biscribed Pentakis Dodecahedron and its elements

Biscribed Pentakis Dodecahedron and its elements

Biscribed Pentakis Dodecahedron and its elements

Biscribed Pentakis Dodecahedron and its elements

New Resources

Discover Resources

Discover Topics