Hendecagon Dissections

Author : Gavin Theobald

{3} Triangle
{4} Square
{5} Pentagon
{6} Hexagon
{7} Heptagon
{8} Octagon
{22} Icosidigon
{6/2} Hexagram
{11/2} Hendecagram
{11/3} Hendecagram
{11/4}  Hendecagram
{R×} Optimised Rectangle
{L} Latin Cross
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
11 10 12 1211 15 1615 1


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
15

Triangle — Hendecagon (11 pieces)

This dissection makes two uses of the TT2 method.

Reducing this dissection to 11 pieces was not easy. In the wider hendecagon strip the two large pieces can be varied in size. I vary the size to ensure that a hendecagon edge passes exactly through the intersection of triangle edges at the edge of the triangle strip. This saves a piece. The second overlay diagram shows the initial stage of overlaying the second two strips. I modify the shape of the trapezium of the thinner triangle strip to save a further two pieces.

Square — Hendecagon (10 pieces)

Ernest Irving Freese solved this dissection in 13 pieces.

Greg Frederickson suggested that I tried dissecting the hendecagon to a square. This is my best solution after many attempts. It uses the TT2 method twice.

Pentagon — Hendecagon (12 pieces)

Hexagon — Hendecagon (12 pieces)

Hexagon — Hendecagon (11 pieces with 1 turned over)

Heptagon — Hendecagon (15 pieces)

Octagon — Hendecagon (16 pieces)
Octagon — Hendecagon (15 pieces with 1 turned over)

Hendecagon — Icosidigon {22} (23 pieces)

Hendecagon — Hexagram (15 pieces)

Hendecagon — Hendecagram {11/2} (23 pieces)

Hendecagon — Hendecagram {11/3} (23 pieces)

Hendecagon — Hendecagram {11/4} (23 pieces with 11 turned over)

Discovered by Greg Frederickson (2002).

Hendecagon — Optimised Rectangle (9 pieces)

Hendecagon — Latin Cross (13 pieces)