Cool, are you planing to expand the glossary?
There are some basic shapes missing, for example the coinder, the sphericone and the dicone, some regular/uniform polytopes in 4 and 5D, and toratopes in 5D.
Based on existing toratope names in 4D, I've developed a consistent system of toratope nomenclature based on the geometry.
If you know, how the system works, you could derive the shape from the name despite it being also suited for everyday language and laypeople.
http://hi.gher.space/forum/viewtopic.php?f=24&t=2072&p=25893#p25813
What is deep in our world is superficial in higher dimensions.