These 5 tilings are in two classes. The first two are in the regiments of regulars with an even-sided verf. Taking this verf as a di-n-gon makes demi symmetry and creates a new faceting with hemi-apeirogons. These are like thah. The last three are in the that regiment, which is the rectate of hexat and trat. Rectified squat is just squat. All of these are used in non-prismatic honeycombs.
8: Sha - Square-hemiapeirogonal tiling. Its faces are squares and apeirogons. Symbol is x∞x4o4/3*a. This is in the squat regiment, using half the squares in a sort of checkerboard arrangement. This is very closely related to thah, but since it's wythoffian it shows up significantly more often. Despite having half the symmetry of squat, it still has squattic symmetry. Euclideans are weird. Its vertex figure is a bowtie.
9: Ditatha - Ditrigonary triangular-hemiapeirogonal tiling. Its faces are triangles and apeirogons. Symbol is x3o3/2o∞*a. This is in the trat regiment, using half the triangles. This one has "cyclotriggic symmetry", which is hexattic but all of the hexagonal axes are turned to triangular ones, with other symmetries removed accordingly. This symmetry is not very important in 2D, but hexattics can only be used in 3D nonprismatics if they can take cyclotriggic subsymmetry. Its vertex figure is a hemitripod.
10: That - Trihexagonal tiling. Its faces are triangles and hexagons. Symbols are o3x6o and x3x3o3*a. That is the rectified hexat and the rectified trat. It also has trapezivert subsymmetry under cyclotriggic, which is how it is used in higher dimensions. Its verf is a rectangle.
11: Tha - Triangular-hemiapeirogonal tiling. Its faces are triangles and apeirogons. Symbol is x∞x3o3/2*a. Tha is wythoffian only as a trapezivert. Its verf is a bowtie.
12: Hoha - Hexagonal-hemiapeirogonal tiling. Its faces are hexagons and apeirogons. This is the first nonwythoffian on our list, but hemirectates aren't impressive. Its verf is also a bowtie.
Below shows how the quasiregulars pair up as conjugates.
Conjuates:
The following are self-conjugate: all
The following are conjugate pairs: none
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