Rhombicosidodecahedron, n=60. Polyhedra with extreme distribution of equivalent vertices. Topic: , Centroid or Barycenter , Constructions , Optimization Problems , Geometric Mean , Linear Programming or Linear Optimization , Median Value , Plane Figures or Shapes , Polygons , Solids or 3D Shapes , Special Points , Sphere Volume The coordinates of the polyhedron are taken from the applet: Polyhedra whose vertices are equivalent and have an extreme distribution on the same sphere.
The first applet sorts and finds the vertices, surface segments, faces, and volume of the polyhedron and its dual image.
The second applet colors the edges and faces of the polyhedron and its dual image.
All applets are in the Book: Polyhedra with extreme distribution of equivalent vertices :
Polyhedra whose vertices are equivalent and have an extreme distribution on the same sphere. * n=4: Tetrahedron; n=6: Octahedron; n=8: Cube, Square Antiprism; n=12: Icosahedron, Cuboctahedron,T runcated Tetrahedron; n=20: Dodecahedron; n=24: Biscribed Snub Cube, Truncated Cube, Biscribed Truncated Octahedron; n=30: Icosidodecahedron; n=48: Biscribed Truncated Cuboctahedron; n=60: Biscribed Snub Dodecahedron, Rhombicosidodecahedron, Biscribed Truncated Icosahedron, Truncated Dodecahedron; n=120: Biscribed Truncated Icosidodecahedron.
This extreme distribution is obtained by me in the
Vertices: 60 (60) Faces: 62 (20 equilateral triangles + 30 squares + 12 regular pentagons) Edges: 120 applet- "Three-parameter model transformations of the Icosahedron faces."(Special Case 13). Maximization of the average distance between the vertices was performed using one parameters: q.