  The closed Friedmann--Lema\^itre--Robertson--Walker (FLRW) universe of
Einstein gravity with positive cosmological constant in three dimensions is
investigated by using the Collins--Williams formalism in Regge calculus. A
spherical Cauchy surface is replaced with regular polyhedrons. The Regge
equations are reduced to differential equations in the continuum time limit.
Numerical solutions to the Regge equations approximate well the continuum FLRW
universe during the era of small edge length. The deviation from the continuum
solution becomes larger and larger with time. Unlike the continuum universe,
the polyhedral universe expands to infinite within finite time. To remedy the
shortcoming of the model universe we introduce geodesic domes and
pseudo-regular polyhedrons. It is shown that the pseudo-regular polyhedron
model can approximate well the results of the Regge calculus for the geodesic
domes. The pseudo-regular polyhedron model approaches the continuum solution in
the infinite frequency limit.
