 
Summary: The Isometry Dimension and
Orbit Number of a Finite Group
Michael O. Albertson
Department of Mathematics
Smith College, Northampton, MA 01063
albertson@math.smith.edu
Debra L. Boutin
Department of Mathematics
Hamilton College, Clinton, NY 13323
dboutin@hamilton.edu
Abstract
A finite set W Rd
is said to realize the group G if
the isometry group of W is isomorphic to G. The isometry
dimension of a group is the minimum dimension of a real
ization. It is known that the isometry dimension of G is less
than G [1]. We show that the isometry dimension of Zn
2
is n. The orbit number of a group is the minimum number
of orbits in a realization. We show that the groups Zn
