Symmetrohedra are polyhedra which have many (but not all) faces regular, and have some form of polyhedral symmetry. Here’s one that has regular decagons and triangles, along with trapezoids appearing in “bowtie” pairs.

The next one has regular dodecagons and decagons, along with trapezoids which closely resemble triangles, and some very thin rectangles.

Finally, in the last of these three, the regular faces are dodecagons and pentagons. For the irregular faces, there are two different types of trapezoids.

All three of these were made with Stella 4d, which you can try for free right here.