The Mathematical Institute at the University of Oxford runs a series of masterclasses for Year 9-Year 11 students each year, with the aim to inspire and engage young people in the practice and art of maths. On Saturday 29 January 2022, Yvonne Scott and Alex Neville from the AMSP ran a Year 9 masterclass titled *Graphs But Not As You Know It*. This session focused on introducing around 50 students to some discrete maths.

The talk began with Yvonne explaining networks and their practical uses, for example in computing and transport efficiency. She discussed the differences between Euler and Hamiltonian Paths/Cycles and the uses of this theory, such as in solving the Bridges of Königsberg problem.

Alex then introduced Schlegel diagrams, which give 2D representations of 3D shapes. The students were asked to produce a Hamiltonian Cycle of the diagram for a dodecahedron, using three different colours.

Using their diagram, the students had to produce a 3D origami dodecahedron with ten sheets of three different colours of paper. No two pieces of the same colour were allowed to meet at a vertex. The pictures shown are examples of the students’ finished work.

The session was great fun and the paper explosion allowed the students to see that maths is creative, fun, and not always about numbers! Hopefully this masterclass will have inspired some students to consider taking A level Further Mathematics.