These 4 tilings are formed by truncating and quasitruncating regular tilings. Two are truncates, two are quasitruncates. Squat and hexat, having even-sided faces, can both be truncated and quasitruncated. Trat can only be truncated, but this results in a subsymmetrical hexat, and thus produces no new tilings. All of them have isosceles triangle vertex figures. Tosquat and quitsquat are used in non-prismatic honeycombs, toxat and quothat not so much.
4: Tosquat - Truncated square tiling. Its faces are squares and octagons. Symbols are x4x4o, x4x4x. This has subsymmetry as an omnitruncate which is used frequently.
5: Toxat - Truncated hexagonal tiling. Its faces are triangles and dodecagons. Symbol is x6x3o. This is our first introduction to dodecagons! As a rule of thumb, anything with dodecagons in its edges is never used in higher dimensions (as far as we know!).
6: Quitsquat - Quasitruncated square tiling. Its faces are squares and octagrams. Symbols are x4/3x4o, x4/3x4/3x. This, like its conjugate, also has an often occurring subsymmetry as an omnitruncate.
7: Quothat - Quasitruncated hexagonal tiling. Its faces are triangles and dodecagrams. Symbol is x6/5x3o. Just like dodecagons, dodecagrams seem to outlaw a tiling from higher dimensional usage. This tiling gets the "most spikiest" award, for being very very spiky. Dodecagrams have such a thin angle that all tilings involving them usually end up atleast a little spiky.
Below shows how the truncates pair up as conjugates.
Conjuates:
The following are self-conjugate: none.
The following are conjugate pairs: squat-quitsquat, toxat-quothat.
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