Primitive Perfect Isosceles Right Triangled Square

Title: __ 19:216DQ GHM

Order: 19

Horizontal side: 216 Vertical side: 216

Elements: 1√2, 2, 2√2, 4, 4√2, 7√2, 14, 11√2, 22, 25√2, 50, 50√2, 72, 83, 94, 72√2, 83√2, 133, 144.

Code: 1445 0 72 1331 133 216 837 133 216 836 133 133 252 158 108 143 158 94 72 165 101 10 165 101 20 164 100 21 166 100 502 216 50 40 162 98 41 166 98 116 133 83 227 144 94 943 166 0 725 0 0 724 72 0 503 216 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)

144
133
83
83√2
25√2
14
7√2
1√2
2√2
2
50√2
4√2
4
11√2
22
94
72
72√2
50