Q: Can a regular pentagon and two regular hexagons meet at a vertex of a tessellation?

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Three regular hexagons meeting at a vertex would form a tessellation. So they would form a plane not a solid.

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).

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!

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

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Three regular hexagons meeting at a vertex would form a tessellation. So they would form a plane not a solid.

Yes. Regular or irregular, the angles at vertices must sum to 360 deg otherwise you will have gaps in the tessellation.

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.

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).

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!

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

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.

In a regular pentagon, the lines of symmetry are drawn from each vertex to the midpoint of the edge directly opposite the vertex, so there are five in all.

A semi-regular tessellation is covering a plane surface with two or more different regular polygons, all of which have sides of the same length. In addition, each polygon vertex is surrounded by polygons in the same order.

A semi-regular tessellation is covering a plane surface with two or more different regular polygons, all of which have sides of the same length. In addition, each polygon vertex is surrounded by polygons in the same order.