Facial Sums

Can you make the numbers around each face of this solid add up to the same total?
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Problem

Image
Facial Sums



The diagram shows a solid with six triangular faces.

At each vertex there is a number and two of the numbers are 1 and 5, as shown.

The sum of the numbers at the three vertices of each face is calculated, and all the sums are the same.

What is the sum of all five numbers at the vertices?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.