Squaring.net >> IRTS >> PPIRTSS >> Order 17

**
Primitive Perfect Isosceles Right Triangled Square
**

**Title:** ___ 17:74AE GHM

**Order:** 17

**Horizontal side:** 74 **Vertical side:** 74

**Elements:** 5, 5√2, 10, 10√2, 12√2, 17, 13√2, 22, 24, 25, 26, 22√2, 23√2, 24√2, 25√2, 26√2, 39.

**Code:** 265 0 48 264 26 48 393 52 35 227 52 74 226 52 52 175 52 35 242 24 24 134 13 35 234 36 12 100 59 35 101 69 35 52 74 30 53 74 25 250 49 25 251 74 25 243 24 0 122 36 12

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)

26

26√2

39

22

22√2

17

24√2

13√2

23√2

10√2

10

5√2

5

25√2

25

24

12√2