three identical pyramids build a cube

four regular pyramids and a regular tetrahedron build a cube 
see also the decomposition of the cube into six SchlĂ¤flis' birectangular tetrahedra


rhombic dodecahedron: cube augmented with six pyramids
the six pyramids fill exactly the cube (the ratio of the volumes is exactly 2) 
regular dodecahedron: cube augmented with six "roofs"
the hole in the cube is a curious dodecahedron (the ratio of the volumes is about 1.927)  
These two objets are not very difficult to carry out. Here are technical data useful to build them:


Be patient during the initialization! (reload the page if an animation doesn't start)
home page

convex polyhedra  non convex polyhedra  interesting polyhedra  related subjects  February 2000 updated 18012009 