enclosing

this page gathers links to explorations of how the convex regular polyhedra (aka the Platonic solids) can be inscribed in one another, as well as how the Archimedean solids and concave regular polyhedra fit inside them, presenting their configurations with diagrams and explanations of the underlying geometric relations:

• enclosing inside the tetrahedron
  • tetrahedron inside the tetrahedron
  • octahedron inside the tetrahedron
  • icosahedron inside the tetrahedron
  • cube inside the tetrahedron
  • dodecahedron inside the tetrahedron
  • the Archimedeans solids inside the tetrahedron
• enclosing inside the regular octahedron
  • regular facets of the octahedron
  • tetrahedra inside the octahedron
  • icosahedra inside the octahedron
  • cubes inside the octahedron 01
  • cubes inside the octahedron 02
  • dodecahedra inside the octahedron
• enclosing inside the regular icosahedron
  • regular facets of the icosahedron
  • tetrahedra inside the icosahedron
  • octahedra inside the icosahedron
  • cubes inside the icosahedron
  • dodecahedron inside the icosahedron
  • small stellated dodecahedron inside the icosahedron
  • great dodecahedron inside the icosahedron
  • great icosahedron inside the icosahedron
• enclosing inside the regular hexahedron (cube)
  • regular facets of the cube
  • tetrahedra inside the cube
  • octahedron inside the cube 01
  • octahedra inside the cube 02
  • icosahedra inside the cube
  • dodecahedra inside the cube 01
  • dodecahedron from the cube 02
• enclosing inside the regular dodecahedron
  • regular facets of the dodecahedron
  • tetrahedra inside the dodecahedron
  • cubes inside the dodecahedron
  • octahedra inside the dodecahedron
  • icosahedron inside the dodecahedron
  • great stellated dodecahedron inside the dodecahedron