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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.

Q: What is a tessellation vertex?

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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.

Semi-regular tessellation is a tessellation of the plane by 2 or more different convex regular polygons. A semi-regular tessellation combines two or more regular polygons. Each semi-regular tessellation has a tupelo, which designates what kind of regular polygon is used.