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## 'Icosagram' printed from http://nrich.maths.org/

This problem was written by James from St Peter's College,
Adelaide, Australia.

Draw a pentagon and draw in all the diagonals (lines joining the
vertices not including the edges of the pentagon), how many
diagonals is this?

This is called a pentagram. How many diagonals are there in a
hexagram, heptagram, octagram, nonagram, decagram etc. up to a 20
sided shape.

Does any pattern occur when looking at the number of
diagonals?

Why is this so?

Can you find a formula?