  This paper considers passing from the usual $\mathbb{R}^d$ model of absolute
space to $\mathbb{S}^d$ at the level of relational particle models. Both
approaches' $d = 1$ cases are rather simpler than their $d \geq 2$ cases, with
$N$ particles in $\mathbb{S}^1$ admitting a straightforward reduction with
shape space $\mathbb{T}^{N - 1}$. The $\mathbb{S}^2$ and $\mathbb{S}^3$ cases -
observed skies and the simplest closed GR cosmologies respectively -- are also
considered, the latter in the contexts of both static and dynamical radius of
the model universe. The space of relational triangles on $\mathbb{S}^2$ is
hyperbolic 3-space $\mathbb{H}^3$. Overall, by passing to a closed underlying
absolute space, and then to dynamical notion of space, we close some of the
modelling gaps between relational particle models and geometrodynamics or its
inhomogeneous perturbative regime of interest in cosmology. Quantum
counterparts are also outlined, for use as model arenas of quantum cosmology.
These models are useful in further considerations of both classical and quantum
background independence.
