Dodecamagic

Here you see the front and back views of a dodecahedron which is a solid with pentagonal faces.

Using twenty of the numbers from 1 to 25, each vertex can be numbered so that the numbers around each pentagonal face add up to 65.

The number F is the number of faces of the solid.
You might like to draw the net of a dodecahedron, or download the net here, and write the numbers at the vertices, or make the solid and write the numbers on it. Can you find all the missing numbers?

Click here to download the DODECAMAGIC worksheet.

Click here for Notes for Teachers.

This problem is adapted from the NRICH task of the same name with permission of the University of Cambridge. All rights reserved.