Quasiregular polytope

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This definition here is based on Coxeter citation needed. (It should be noted however, that this very term simply states "nearly regular". And as such it well is in use for a varity of further readings. One of those different ones eg. simply assumes that a single node of its Coxeter-Dynkin diagram would be ringed only.)

A quasiregular polytope is any polytope with regular facets and quasiregular vertex figures. They are vertex-transitive and have two types of alternating facets.[1] They are ridge-transitive. In 3d they compose of mostly rectified uniforms and hemipolyhedra. Any regular-faceted two-orbit polytope is quasiregular. In more than 2 dimensions, they are uniform. However in 2D, they are usually just semi-uniform. All non-compound quasiregular polytopes are two-orbits, and all regular-faced two-orbits are quasiregular. In two dimensions they are semi-uniform polygons with either one or two edge lengths and an even number of sides/vertices.

A list an be found here