Uniform Self-Dual Non-Regular Polytope

[Mecejide]

I have discovered that the great icosiheptapeton (gaje) is uniform and self-dual, but not regular.

[Klitzing]

just for recap: what is gaje?
--- rk

[username5243]

Gaje (great icosaheptapeton) is one of three noble members of the jak regiment (it's number 162 on http://www.polytope.net/hedrondude/primary6.htm). Its facets are 27 hits (which is in turn the noble member of the hin regiment).

[Catisfluffy]

Are there any examples in lower dimensions?

[mr_e_man]

I thought of some tilings on a flat torus (with unequal length and width), but I later realized that the faces are not regular, depending on definitions (local vs global isometries; whether a square can rotate 90° when the space itself cannot).

Anyway, you were probably looking for something in Euclidean space, not on a flat torus....