Časopis pro pěstování matematiky, roČ. 101 (1976), Praha 24 SELF-INSCRIBED DECAGONS IN DESARGUES CONFIGURATION 10,

In this note we shall show that the Desargues configuration 103 can be regarded as a set of 24 self-inscribed decagons having a certain group structure. The Desargues configuration 103 is a figure of 10 lines and 10 points, 3 points on each line and 3 lines through each point. 0 The existence of this configuration is a consequence of the Desargues theorem which states: If two triangles are perspective from a point then they are perspective from a line. This configuration can be regarded in 10 ways as a pair of triangles in perspective, since every pair of triangles formed by the points ifc, il, im and jkjljm are perspec tive from the vertex ij and the side klm. The Desargues configuration reveals five pairs of quadrangles and quadrilaterals, 232 the latter inscribed into the former. The six sides, ijk9 ilm9 ikl9 imj9 ijl9 ikm9 of every quadrangle pass, respectively, through the six vertices jk9 lm9 kl9jm9jl9 km9 of th