from the cube 
from the cube 
from the regular dodecahedron 
We may also assemble in the same manner regular pyramids on the faces of the three regular polyhedra with triangular faces.


The pyramids to be assembled on the octahedron are quarters of a regular tetrahedron (apex of the pyramid at the tetrahedron's center); those to be assembled on the cube (animation above on the left) are sixths of a cube. 

And what do we get if we assemble likewise regular pyramids on the faces of a regular tetrahedron?  
from the regular octahedron to the rhombic dodecahedron 
Let us think about it: two lateral faces of two adjacent pyramids are coplanar... and build a rhombus... How many rhombi?
Try to recognize this very well known polyhedron. 
from the regular icosahedron to the rhombic triacontahedron 
Be patient during the initialization! (reload the page if an animation doesn't start)
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convex polyhedra  non convex polyhedra  interesting polyhedra  related subjects  April 2002 updated 12122004 