Hole Dissections

Author : Gavin Theobald

[3]—[4]	Triangle — Square
[3]—[5]	Triangle — Pentagon
[3]—[6]	Triangle — Hexagon
[3]—[7]	Triangle — Heptagon
[3]—[8]	Triangle — Octagon
[3]—[10]	Triangle — Decagon
[3]—[12]	Triangle — Dodecagon
[3]—[5/2]	Triangle — Pentagram
[3]—[6/2]	Triangle — Hexagram
[3]—[8/3]	Triangle — Octagram
[3]—[12/2]	Triangle — Dodecagram
[4]—[5]	Square — Pentagon
[4]—[6]	Square — Hexagon
[4]—[7]	Square — Heptagon
[4]—[8]	Square — Octagon
[4]—[9]	Square — Enneagon
[4]—[10]	Square — Decagon
[4]—[12]	Square — Dodecagon
[4]—[5/2]	Square — Pentagram
[4]—[6/2]	Square — Hexagram
[4]—[8/2]	Square — Octagram
[4]—[8/3]	Square — Octagram
[4]—[12/2]	Square — Dodecagram
[5]—[6]	Pentagon — Hexagon
[5]—[8]	Pentagon — Octagon
[5]—[10]	Pentagon — Decagon
[5]—[6/2]	Pentagon — Hexagram
[5]—[8/3]	Pentagon — Octagram
[6]—[7]	Hexagon — Heptagon
[6]—[8]	Hexagon — Octagon
[6]—[10]	Hexagon — Decagon
[6]—[12]	Hexagon — Dodecagon
[6]—[5/2]	Hexagon — Pentagram
[6]—[6/2]	Hexagon — Hexagram
[6]—[8/3]	Hexagon — Octagram
[6]—[12/2]	Hexagon — Dodecagram
[8]—[10]	Octagon — Decagon
[8]—[6/2]	Octagon — Hexagram
[8]—[8/3]	Octagon — Octagram
[10]—[5/2]	Decagon — Pentagram
[10]—[6/2]	Decagon — Hexagram
[10]—[8/3]	Decagon — Octagram
[5/2]—[6/2]	Pentagram — Hexagram
[5/2]—[8/3]	Pentagram — Octagram
[6/2]—[8/3]	Hexagram — Octagram

3
3	4
5	4	5
4	3	5	6
6	6		6	7
5	3	6	5		8
	6					9
5	4	6	5		6		10
6	4		4					12
5	5		5				5		5/2
3	4	6	5		6		6		6	6/2
	5										8/2
5	4	6	5		5		6		6	6		8/3
5	6		6										12/2

Triangle — Square (3 pieces)

The dissection is hingeable.

Triangle — Pentagon (5 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Triangle — Hexagon (4 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Triangle — Heptagon (6 pieces)

Triangle — Octagon (5 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Triangle — Decagon (5 pieces)

Triangle — Dodecagon (6 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Triangle — Pentagram (5 pieces)

Triangle — Hexagram (3 pieces)

Triangle — Octagram [8/3] (5 pieces)

Triangle — Dodecagram [12/2] (5 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Square — Pentagon (4 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Square — Hexagon (3 pieces)

The dissection is translational. The pieces can be rearranged simply by sliding them one at a time, without rotation, and without any piece ever overlapping another.

Square — Heptagon (6 pieces)

Square — Octagon (3 pieces)

Square — Enneagon (6 pieces)

Square — Decagon (4 pieces)

Square — Dodecagon (4 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Square — Pentagram (5 pieces)

Square — Hexagram (4 pieces)

The dissection is translational. The pieces can be rearranged simply by sliding them one at a time, without rotation, and without any piece ever overlapping another.

Square — Octagram [8/2] (5 pieces)

This dissection was discovered by Greg Frederickson. This may well be the first hole dissection.

Square — Octagram [8/3] (4 pieces)

Square — Dodecagram [12/2] (6 pieces)

The dissection is translational.

Pentagon — Hexagon (5 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Pentagon — Octagon (6 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Pentagon — Decagon (6 pieces)

Pentagon — Hexagram (6 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Pentagon — Octagram [8/3] (6 pieces)

Hexagon — Heptagon (6 pieces)

Hexagon — Octagon (5 pieces)

The pieces can be rearranged simply by sliding them one at a time and without any piece ever overlapping another.

Hexagon — Decagon (5 pieces)

Hexagon — Dodecagon (4 pieces)

Hexagon — Pentagram (5 pieces)

Hexagon — Hexagram (5 pieces)

The dissection is translational. The pieces can be rearranged simply by sliding them one at a time, without rotation, and without any piece ever overlapping another.