Quasiregular polytope

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. 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.

2D
There are an infinite number of quasiregular polygons. They are any polygon that have two edge lengths and are vertex-transitive. The ones that occur in the verfs of 3d quasiregulars are the:

-Rectangle

-Bowtie

-Propeller tripod

-Ditrigon and the

-Tripod

3D
Rectified regular polyhedra are quasiregular. This is not true in higher dimensions, where they are usually just uniform. These are the:

-Tetratetrahedron (rectified tetrahedron)

-Cuboctahedron (rectified cube/octahedron)

-Icosidodecahedron (rectified icosahedron/dodecahedron)

-Trihexagonal tiling (rectified triangular tiling/hexagonal tiling)

-Square tiling (rectified square tiling)

-Great icosidodecahedron (rectified great stellated dodecahedron/great icosahedron)

-Dodecadodecahedron (rectified small stellated dodecahedron/great dodecahedron)

The Triangular tiling can also be seen as quasiregular.

Some hemipolyhedra are also quasiregular. These are the:

-Tetrahemihexahedron

-Octahemioctahedron

-Cubohemioctahedron

-Small icosihemidodecahedron

-Small dodecahemidodecahedron

-Great icosihemidodecahedron

-Great dodecahemidodecahedron

-Small dodecahemicosahedron and the

-Great dodecahemicosahedron

Finally, there are four quasiregular polyhedra that are neither. These are the

-Ditrigonary dodecadodecahedron

-Small ditrigonal icosidodecahedron and the

-Great ditrigonary icosidodecahedron

4D
In 4 dimentions, there are just a few quasiregulars. These are the:

-Tetrahedral-octahedral honeycomb

-Cubic honeycomb

-Hexadecachoron

-Tesseractihemioctachoron

-Small ditrigonary hexacosihecatonicosachoron

-Great ditrigonary hexacosihecatonicosachoron and the

-Ditrigonary dishecatonicosachoron

5D+
In 5+ dimentions, there are just a few quasiregulars. In each dimension there is the hypercubic honeycomb, orthoplex, and the demicross.