The regular star-polyhedron
$\left\{ 5,\,\frac{5}{2} \right\}$
is isomorphic to the abstract polyhedron
$\left\{ 5,\,5|3 \right\}$
, where the last entry “3” in its symbol denotes the size of a hole, given by the imposition of a certain extra relation on the group of the hyperbolic honeycomb
$\left\{ 5,\,5 \right\}$
. Here, analogous formulations are found for the groups of the regular 4-dimensional star-polytopes, and for those of the non-discrete regular 4-dimensional honeycombs. In all cases, the extra group relations to be imposed on the corresponding Coxeter groups are those arising from “deep holes”; thus the abstract description of
$\left\{ 5,\,{{3}^{k}},\,\frac{5}{2} \right\}\,\text{is}\,\left\{ 5,\,{{3}^{k}},\,5|3 \right\}\,\text{for}\,k\,=\,1\,\text{or}\,\text{2}$
. The non-discrete quasi-regular honeycombs in
${{\mathbb{E}}^{3}}$
, on the other hand, are not determined in an analogous way.