🔺Regular polyhedra are 3D shapes made up of polygons, where all faces, edges, and vertices are the same.
⭐️There are twelve regular polyhedra, including the platonic solids, Kepler-Poinsot polyhedra, regular tilings, and Petrie-Coxeter polyhedra.
🔳Regular tilings are flat and infinitely large, while the Petrie-Coxeter polyhedra are non-flat infinite polyhedra.
How many regular polyhedra are there?
—There are twelve regular polyhedra, including the platonic solids, Kepler-Poinsot polyhedra, regular tilings, and Petrie-Coxeter polyhedra.
What are the platonic solids?
—The platonic solids are 3D shapes made up of regular polygons, including the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
What are the Kepler-Poinsot polyhedra?
—The Kepler-Poinsot polyhedra are regular star polyhedra, including the small and great stellated dodecahedra, and the great dodecahedron and great icosahedron.
What are the regular tilings?
—The regular tilings are infinite flat shapes made up of regular polygons, including the triangular tiling, square tiling, and hexagonal tiling.
What are the Petrie-Coxeter polyhedra?
—The Petrie-Coxeter polyhedra are non-flat infinite polyhedra discovered by John Petrie and Donald Coxeter.
00:00Introduction to regular polyhedra and their characteristics.
05:58Explanation of the platonic solids and their properties.
08:40Introduction to the Kepler-Poinsot polyhedra and their significance.
11:28Overview of the regular tilings and their unique properties.
13:18Introduction to the Petrie-Coxeter polyhedra, including their discovery and characteristics.
