a few nice assemblages

from the cube
to the rhombic dodecahedron

from the cube
to the regular dodecahedron

from the regular dodecahedron
to the rhombic triacontahedron

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 12-12-2004