Q:

Which polyhedron has 17 vertices, 34 edges and 19 faces?

on exam I had task to check that there is polyhedron with 8 triangle faces, 11 quadrangle, each vertices have degree 4. after calculate I obtain that it have 34 edges, 17 vertices and 19 faces but i don't know how to drow it. any ideas? or maybe anyone know online generator for pylohendron. wolfram alfa unfortunately doesn't work for very specific polyhendrons.

A:

Here is the graph of such a polyhedron:

The bluish regions (including the outer region) are quadrangles, and the reddish ones are triangles. As you can see, it meets the given requirements.
I only found this through trial and error and a certain amount of luck. It doesn't seem realistic to me to find such an object on an exam (let alone draw the corresponding polyhedron in 3d?!—surely the graph is enough) unless there is some context we are missing.

EDIT: redrew graph to make it 4-regular.

