Primitive Perfect Isosceles Right Triangled Square

Title: _ 20:270AN GHM

Order: 20

Horizontal side: 270 Vertical side: 270

Elements: 10, 10√2, 20, 24, 30, 30√2, 37√2, 60, 62, 74, 86, 61√2, 62√2, 98, 100, 74√2, 86√2, 122, 98√2, 110√2.

Code: 1227 0 270 620 122 270 621 184 270 867 184 270 866 184 184 603 60 148 1007 60 208 1100 160 208 241 184 208 742 74 74 304 30 118 303 60 118 201 50 118 102 60 108 101 60 118 614 111 37 980 172 98 981 270 98 743 74 0 372 111 37

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)