I don't know what a tessellation vertex is but I will try to Answer it I think it means the endpoint of a vertex which is also called vertices,which is the pointy ends of the vertex.
It is 360 degrees.
Gee, Hard problem
Hi im bob
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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
Yes. Regular or irregular, the angles at vertices must sum to 360 deg otherwise you will have gaps in the tessellation.
No. You would need 2.4 such shapes to meet at each vertex and since 0.4 of a 12-gon is impossible, so is the tessellation.
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!
They add to 360 degrees.
The angles at any point is space add to 360 degrees. So, at any vertex in a tessellation, the angles of the vertices meeting there must sum to 360 degrees.
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).