Quasiregular polytope

A quasiregular polytope is any polytope with regular facets and quasiregular vertex figures. They are ridge-transitive. They are vertex-transitive and have two types of alternating facets. They are a subcategory of the uniform polytopes. In 3d they compose of mostly rectified uniforms and hemipolyhedra.

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

-Octahedron (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 three quasregular 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:

-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.