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Overview
In Houdini, geometry is made up of primitives, with the most common primitive being a polygonal faces. Each corner of a polygonal face is a vertex. To keep individual faces together as part of a surface, vertices of separate faces can be fused together as a point. When a point moves, Houdini automatically moves each of the pointâ€™s vertices as well.
Geometry traversal

You can use vertexpoint to get from a vertex to its point.

You can use pointvertex to get from a point to its first vertex and vertexnext and vertexprev to iterate through the list of vertices sharing that point.

To iterate through the vertices of a polygonal face, use primvertexcount to get the number of vertices, then you can use the primitive number and a counter from
0
toprimitive count  1
to refer to the vertices. 
A vertex number is the 0based index of a certain vertex of a primitive. A linear vertex number is the 0based index of a certain primitive across all the geometry. It is just a slightly more convenient way to refer to a vertex with one number instead of two (primitive number and vertex number). You can use vertexindex to get a linear vertex number from a primitive number and a vertex number. Use both vertexprim and vertexprimindex to convert the other way, from a linear vertex number to a primitive number and a vertex number.
Returns 
Function 
Argument(s) 

Point number 
Linear vertex number  
Linear vertex number 
Point number  
Linear vertex number 
Linear vertex number  
Linear vertex number 
Linear vertex number  
Linear vertex number 
Primitive number, Vertex number 

Number of vertices 
Primitive number  
Primitive number 
Linear vertex number  
Vertex number 
Linear vertex number 