A ‘magic’ hexagon has rows of numbers in three directions that add to the same total. It is possible to construct such a hexagon from a honeycomb array of hexagons and from an array of triangles (Figure 1). There is known to be only one magic hexagon formed from hexagons. However, numerous magic arrangements are possible for the hexagon of triangles and these arrangements have many additional interesting properties. In this article we give the reasons why such configurations are possible, we look at the number of arrangements possible when there are 2 triangles on each side of the hexagon and we show that in general the arrangements are balanced in many ways – including that they are physically balanced, a property we call ‘magic moments’.