An array of wooden tiles assembled into an intriguing
pattern flecked with stars forms a striking contrast to the regular arrangement of bricks making up the
wall on which it hangs on the third floor of Avery Hall, home of the mathematics department at the University of
Nebraska-Lincoln.

Constructed by Nebraska mathematician Earl S. Kramer from diamond-shaped
cherry and maple tiles and installed in March 2005, the wall piece represents a patch of one
of the infinite number of ways in which to arrange fat and skinny diamonds into
an aperiodic pattern characteristic of a Penrose tiling.

The two types of tiles for assembling such a Penrose tiling are
rhombs (each rhomb has four sides of equal length) with acute angles of 36 and
72 degrees. Matching rules specify the ways in which these rhombs must be
assembled edge to edge to create an aperiodic tiling (one in which the tiling cannot
be lifted and placed back onto itself with all points displaced but still looking the
same).

The particular tiling pattern depicted in the wall piece is
one of two Penrose rhomb arrangements that have the dihedral automorphism group
d5, featuring
rotations of order five and reflections across a line, readily apparent in the
design.

For another artistic representation of a Penrose tiling, see "Tessellation Tango."

**Reference:**

Peterson, I. 2001.

*Fragments of Infinity: A Kaleidoscope of Math and Art*. Wiley.
Photos by I. Peterson