  We investigated the double-exchange spin ice (DESI) model on a kagom\'e
lattice by Monte Carlo simulation to study the effects of a geometrical
frustration, and the mechanism that generates an ordered state in a metallic
system. The DESI model on the kagom\'e lattice is a frustrated metallic system
due to an effective ferromagnetic interaction between localized spins caused by
the double-exchange (DE) mechanism and a uniaxial anisotropy for the localized
spins. A dodecagonal spin cluster (named dodecamer), which consists of twelve
localized spins, appears at low temperature when the number of particles per
site $n \simeq 1/3 \sim 1/2$. Such a dodecamer order is driven by both the
kinetic energy gain due to the DE mechanism and the geometrical frustration. We
discuss that cluster orders, in general, may be a common feature in itinerant
electron systems coupled with frustrated adiabatic fields.
