Primitive Perfect Isosceles Right Triangled Square
Title: _ 20:264AD GHM
Order: 20
Horizontal side: 264 Vertical side: 264
Elements: 12√2, 16√2, 24, 32, 32√2, 48, 38√2, 66, 48√2, 68, 76, 54√2, 84, 90, 76√2, 108, 112, 84√2, 90√2, 108√2.
Code: 1085 0 156 1084 108 156 1123 216 152 487 216 264 486 216 216 322 248 184 323 248 152 162 264 168 846 180 84 665 0 90 544 54 102 386 66 114 767 104 152 766 104 76 687 180 152 126 54 102 245 66 90 907 0 90 900 90 90 845 180 0
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)