THE FISHER-PEGG MITRE SYSTEM

This tiling is patented by Adrian Fisher -  www.mazemaker.com and Edd Pegg Jr. - www.mathpuzzle.com. Used with permission.

http://www.mathpuzzle.com/Mitre.html

This tiling use tree types of tiles : 

THE PYRAMID has an area of .  It has sides of  1 (x3) and

THE MITRE has an area of .  It has sides of 1 (x2), (x2), and

THE FIN has an area of .  It has sides of 1(x2), , and .

Bands
Dodecagons
Hexagons
Periodic tilings

(6 10, 6 10) squares
(8 16, 8 16) squares
(12 8, 12 8) squares
(12 12, 12 12) squares
(12 16, 12 16) squares
(16 16, 16 16) squares - more than 15000 solutions

Infinite attempts

A = sqrt(3)/4
B = 1/4

x = a_xA + b_xB
y = a_yA + b_yB

(a_x b_x, a_y b_y) - (fins, pyramids, mitres)

(4 0, 4 0)  (4 0 0)	(4 4, 2 2) (2 2 1)	(4 4, 2 6) (2 6 1)	(4 8, 4 4) (4 8 2)

(4 8, 4 8) - (4 16 0)	(6 6, 6 6) - (8 12 3)	(8 4, 8 4) - (12 16 0)

(10 6, 4 4) - (8 12 2)	(8 12, 4 4) - (8 12 4)	(6 18, 4 4) - (8 12 6)

(10 6, 6 6) - (14 12 6)	(6 14, 2 6) - (6 12 2)	(8 8, 6 6) - (10 18 3)

(6 10, 10 10) - (14 28 6)	(6 10, 10 10) - (14 28 6)	(6 10, 10 10) - (14 28 6)	(6 10, 10 10) - (14 28 6)

(4 12, 4 12) - (10 18 3)	(4 12, 4 12) - (12 12 6)	(6 10, 6 10) - (10 22 4)

(8 8, 8 8) - (14 22 5)	(8 8, 8 8) - (16 16 8)	(8 8, 8 8) - (14 22 5)

(12 4, 12 4) - (32 16 4)	(12 8, 12 8) - (28 40 4)

(8 12, 8 12) - (12 48 0)	(8 12, 8 12) - (12 48 0)	(8 12, 8 12) - (12 48 0)

(8 16, 8 16) - (16 64 0)	(12 12,12 12) - (32 48 12)	(12 16, 12 16) - (36 64 16)

(16 16, 16 16) - (56 88 20)

Squares

*  possible
#  possible composed
-  impossible

Home