# Prime Rectangles for Tetrakings

## Introduction

A tetraking or tetraplet is a figure made of four squares joined along edges or diagonally at corners. There are 22 tetrakings, not distinguishing reflections and rotations.

A prime rectangle for a tetraking is a rectangle that the tetraking can tile, that cannot be tiled by smaller rectangles that the tetraking can tile. Here I show known prime rectangles for the tetrakings that are not also tetrominoes. For prime rectangles for tetrominoes and other polyominoes, see Michael Reid's Rectifiable Polyomino Page.

 2×4 8×9 5×16 5×24. None. 2×4 8×9 5×16 5×72 7×24. 2×4. 14×36 14×48 14×60 18×36 18×48 18×52 18×56 18×60 18×64 18×68 18×76 18×80 19×48 19×72 20×30 20×36 20×42 20×48 20×54 21×32 21×40 21×48 21×56 22×36 22×48 22×60 23×48 23×72 24×28 24×30 24×32 24×33 24×34 24×35 24×36 24×37 24×38 24×39 24×40 24×41 24×42 24×43 24×44 24×45 24×46 24×47 24×48 24×49 24×50 24×51 24×52 24×53 24×54 24×55 24×57 24×59 25×48 25×72 26×36 26×48 26×60 27×32 27×40 27×48 27×56 28×30 28×42 29×48 29×72 30×32 30×36 31×48 31×72 32×33 32×39 33×40 39×40. Completed by Toshihiro Shirakawa, 2015. 4×4 8×10 8×13 8×19 10×20 11×16 11×24 12×14. 8×12 8×15 8×16 8×18 8×19 8×20 8×21 8×22 8×23 8×25 8×26 8×29 9×16 9×24 10×12 10×16 10×20 11×16 11×24 12×12 12×14 13×16 13×24 14×16 14×20. Completed by Toshihiro Shirakawa, 2015. 2×4 7×8. 2×4. 4×4. 2×4. None. None. None. None. None. None.

Last revised 2017-10-11.

Back to Polyform Tiling < Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]