  Higher dimensional closed Friedmann-Lema\^itre-Robertson-Walker (FLRW)
universe with positive cosmological constant is investigated by Regge calculus.
A Cauchy surface of discretized FLRW universe is replaced by a regular polytope
in accordance with the Collins-Williams (CW) formalism. Polytopes in an
arbitrary dimensions can be systematically dealt with by a set of five integers
integrating the Schl\"afli symbol of the polytope. Regge action in continuum
time limit is given. It possesses reparameterization invariance of the time
variable. Variational principle for edge lengths and struts yields Hamiltonian
constraint and evolution equation. They describe oscillating universe in
dimensions larger than three. To go beyond the approximation by regular
polytopes, we propose pseudo-regular polytopes with fractional Schl\"afli
symbols as a substitute for geodesic domes in higher dimensions. We examine the
pseudo-regular polytope model as an effective theory of Regge calculus for the
geodesic domes. In the infinite frequency limit, the pseudo-regular polytope
model reduces to the continuum FLRW universe.
