On regular figures in normed planes (Q717842)

The author studies a special class of so-called hexagonal normed planes which are not strictly convex. She introduces the orthocenter of a triangle in the sense of Asplund and Grünbaum. The AG-regular triangle whose orthocenter and circumcenter coincide and the equilateral triangle are different notions in the case of strictly convex normed planes. In the paper under review it is shown that the set of AG-regular triangles coincides with the set of equilateral triangles for the case of hexagonal normed planes. It is also proved that the outer Napoleon triangle is equilateral in a hexagonal normed plane.