Primitive Perfect Isosceles Right Triangled Square
Title: __ 18:178AD GHM
Order: 18
Horizontal side: 178 Vertical side: 178
Elements: 2, 8, 6√2, 10, 8√2, 12, 10√2, 22, 28, 25√2, 28√2, 50, 50√2, 72, 78, 75√2, 78√2, 128.
Code: 1287 0 178 280 128 178 281 156 178 102 166 168 221 178 178 103 166 158 125 166 156 87 156 158 80 164 158 21 166 158 64 172 150 786 100 78 756 25 75 727 100 150 785 100 0 250 25 75 507 0 50 500 50 50
The properties below may precede order:side in a tiling's title:
- c = crossed. There is a tile-corner traversed by two lines. The only known crossed PPIRTS's below order 20 are 19:35AB1of4 and 19:35AB4of4.
- d = double-pentagon patterned. Every such tiling is a subdivision of an instance of the same deformable tiling by two 45-90-90-90-225 pentagons with a shared side, four triangles and two pseudotriangles. All below order 19 are degenerate in the sense that one or more sides of underlying tiles have shrunk to zero length. The non-degenerate d-tilings of order 19 are 19:221AA, 19:229AB and 19:241AA.
- e = elegant. No tile-corner is just a T-junction. Such tilings may be considered aesthetically pleasing. The only known elegant PPIRTS's below order 16 are 13:21AA, 14:26AJ, 14:35AA and 15:55AA.
- i = isomers exist which are ineligible for this catalogue. They are not included in the isomer count which follows 'of' in the tiling id.
- r = rectangular inclusion. The only known PPIRTS's below order 16 with a rectangular inclusion are 13:18AA1-4of4 and 15:44AA1-4of4.
Credit for Discovery
Just three people are credited with the discovery of Primitive Perfects:
Geoffrey H. Morley (GHM, England)
Jasper D. Skinner, II (JDS, United States)
William T. Tutte (WTT, Canada, 1917-2002) (15:44AI, 17:136AJ and 19:56AJ only)