The question cannot be answered because it is based on the incorrect assertion that a semi-regular tessellation does not work. Sorry, but it does work!
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A regular tessellation is based on multiple copies of the same regular polygon. A semi-regular tessellation uses copies of two (or more) regular polygons. In the latter case, at each vertex the various polygons are arrayed in the same order (or its mirror image).
Tessellations are named based on the number of polygons located at a vertex. For example: A regular tessellation, made from only triangles is named 3.3.3
They add to 360 degrees.
Three regular hexagons meeting at a vertex would form a tessellation. So they would form a plane not a solid.