I tried to make a symmetrohedron using regular octadecagons and regular decagons, but that combination forces the octadecagons to overlap, and that causes the would-be symmetrohedron to be non-convex.

I tried to augment these octadecagons with antiprisms, and then form the convex hull of the result. Here’s what I found:

I made these using Stella 4d, which you can try for free right here.