Geometric Dissections

Author : Gavin Theobald

Home

All bright yellow entries in these tables are for dissections that I have discovered myself. Some of these have also been independently discovered by others or others have found different dissections requiring the same number of pieces.

Italic entries on a pale yellow background were discovered by others and I have been unable to find an alternative dissection in the same number of pieces.

Where there are two entries in the tables, the first entry requires pieces to be turned over.

Polygon/Polygram Dissections: {m}-{n}

{3}
4 {4}
6 6 {5}
5 5 7 {6}
8 7 9 8 {7}
7 5 8,9 7,8 10,11 {8}
8 9 10 10,11 13 12 {9}
7 7 9 8,9 11 10 13 {10}
11 10 12 11,12 15 15,16 {11}
8 6 10 6 11 10 13,14 11,12 {12}
7 7 9 9 11 10 14 6 12 {5/2}
5 5 8 6 9 8 11 9 15 9 10 {6/2}
9 7 11 10 13 11 15 13 9 14 11 {8/2}
8 8 9 8,9 12 6 13 12 12 13 10 14 {8/3}
10 9,10 7 10,11 13,14 12,13 17 14 14 15 13 16 14 {10/2}
6 8 11,12 8 11 12 14 12 12,13 14 9 13 13,14 17 {12/2}
4 3 6 5 7 6 9 6 10 7 7 5 8 7 10 9 {R}
5 4 7 7 9 8 11 10 12,13 6 10 8 8 10 13 10 5 {G}
5 5 8 6 8 8 10 10 13 7 10 8 10,11 11 13 11 5 7 {L}

Dissections to Triangle, Square, Pentagon and Hexagon to Polygons: {m}-{n}

{3} {4} {5} {6} {7} {8} {9} {10} {11} {12} {13} {14} {15} {16} {17} {18} {19} {20} {21} {22} {24} {26} {28} {30} {36} {54}
{3} 1 4 6 5 8 7 8 7 11 8 12 12
{4} 4 1 6 5 7 5 9 7 10 6 11 10 11 11 12 12 15,16 14 14,15 14 14 15 16 16 16,17 24
{5} 6 6 1 7 9 8,9 10 9 12 10 14 13 14
{6} 5 5 7 1 8 7,8 10,11 8,9 11,12 6 12

Dissections of Triangle, Square, Pentagon and Hexagon to Polygrams: {p}-{m/n}

{5/2} {6/2} {7/2} {7/3} {8/2} {8/3} {9/2} {9/3} {9/4} {10/2} {10/3} {10/4} {12/2} {12/3} {12/4} {12/5}
{3} 7 5 12 9 8 10 10 6
{4} 7 5 10 12 7 8 12 12,13 19 9,10 10,11 10 8 9,10 11 9
{5} 9 8 11 9 7 11,12
{6} 9 6 10 8,9 8,9 11 8

Dissections of Square to Two Identical Polygons: {4}-2×{n}

{3} {4} {5} {6} {7} {8} {9} {10} {11} {12}
{4} 5 4 8 7 11 10 13 10 14 8

Dissections of Square to Two Identical Polygrams: {4}-2×{m/n}

{5/2} {6/2} {7/2} {7/3} {8/2} {8/3} {9/2} {9/3} {9/4} {10/2} {10/3} {10/4} {12/2} {12/3} {12/4} {12/5}
{4} 12 9 10,11 10 14,15

Dissections of Square to Two Different Polygons/Polygrams: {4}-{m}+{n}

{3}
6 {4}
8 7 {5}
8 7 9 {6}
10 9 12 11 {7}
9 8 11 10 13 {8}
10 9 11 11 13 12 {10}
8 7 9 9 11 10 11 {12}
10 10 12 11 14 12 14 11 {5/2}
9 8 10 10 12 11 12 10 12 {6/2}
9 8 11 10 13 12 13 10 13 11 {8/3}

Dissections of Two Polygons to One: {n}-2×{n}

{3} {4} {5} {6} {7} {8} {9} {10} {11} {12} {13} {14} {15} {16}
5 4 9 8,9 10,11 8 16,19 16 23 10 21,25 22,26 24,28 16

Dissections of Two Polygrams to One: {m/n}-2×{m/n}

{5/2} {6/2} {7/2} {7/3} {8/2} {8/3} {9/2} {9/3} {9/4} {10/2} {10/3} {10/4} {12/2} {12/3} {12/4} {12/5}
11 11 12 13 12 18

Home