A polytope \({{ \mathsf {P}}}\) in some euclidean space is called quasi-regular if each facet \({{ \mathsf {F}}}\) of \({{ \mathsf {P}}}\) is regular and the symmetry group \({\mathbf {G}}({{ \mathsf {F}}})\) of \({{ \mathsf {F}}}\) is a subgroup of the symmetry group \({\mathbf {G}}({{ \mathsf {P}}})\) of \({{ \mathsf {P}}}\). Further, \({{ \mathsf {P}}}\) is of full rank if its rank and dimension are the same. In this paper, the quasi-regular polytopes of full rank that are not regular are classified. Similarly, an apeirotope of full rank sits in a space of one fewer dimension; the discrete quasi-regular apeirotopes that are not regular are also classified here. One curiosity of the classification is the difference between even and odd dimensions, in that certain families are present in \({\mathbb {E}}^d\) if d is even, but are absent if d is odd.

多面体\（{{\ mathsf {P}}} \）在一些欧氏空间被称为准规则如果每个小面\（{{\ mathsf {F}}} \）的\（{{\ mathsf {P} }} \）是规则的和对称组\（{\ mathbf {G}}（{{\ mathsf {F}}}）\）的\（{{\ mathsf {F}}} \）是一个子组对称群\（{\ mathbf {G}}（{{\ mathsf {P}}}）\）的 \（{{\ mathsf {P}}} \）。此外，\({{ \mathsf {P}}}\)如果其秩和维数相同，则为满秩。本文对非正则的满秩准正则多胞体进行分类。类似地，满秩的 apeirotope 位于少一维的空间中；不规则的离散准规则 apeirotopes 也归类在这里。分类的一个好奇是偶数和奇数维度之间的差异，因为如果d是偶数，某些族存在于\({\mathbb {E}}^d\) 中，但如果d是奇数则不存在。