Balls and Straws
Diagonals of Polyhedra
Given a convex polyhedron, it is interesting to connect interior edges
Every model on this page was obtained in this way.
This is a famous configuration of five tetrahedra inscribed in a regular
dodecahedron. The dodecahedral edges are orange and each of the five
inscribed tetrahedra has been assigned a unique color:
The Compound of Five Tetrahedra.
This is a famous configuration of 3 rings, no two of which are linked, but
nevertheless comprise a non-trivial link. The rings are represented by the
colors blue, yellow, and red. If these rings are the boundaries of golden
rectangles lying in mutually-perpendicular planes, then the 12 vertices of
the 3 rectangles coincide with those of a regular icosahedron.
The Borromean Rings.
These two miscellaneous models were obtained from the cuboctahedron and the
icosidodecahedron, respectively. The first has 4 inscribed triangles and
the second has 10 inscribed triangles.
Four Triangles in the Cuboctahedron.
Ten Triangles in the Icosidodecahedron.
Index to Balls and Straws
Index to Polyhedra