Three way dissections

Author : Gavin Theobald

{3}-{4}-{5}	Triangle - Square - Pentagon
{3}-{4}-{6}	Triangle - Square - Hexagon
{3}-{4}-{8}	Triangle - Square - Octagon
{3}-{4}-{12}	Triangle - Square - Dodecagon
{3}-{4}-{5/2}	Triangle - Square - Pentagram
{3}-{4}-{6/2}	Triangle - Square - Hexagram
{3}-{4}-{8/2}	Triangle - Square - Octagram
{3}-{4}-{12/2}	Triangle - Square - Dodecagram
{3}-{5}-{6}	Triangle - Pentagon - Hexagon
{3}-{5}-{6/2}	Triangle - Pentagon - Hexagram
{3}-{6}-{8}	Triangle - Hexagon - Octagon
{3}-{6}-{12}	Triangle - Hexagon - Dodecagon
{3}-{6}-{6/2}	Triangle - Hexagon - Hexagram
{3}-{8}-{6/2}	Triangle - Octagon - Hexagram
{3}-{6/2}-{12/2}	Triangle - Hexagram - Dodecagram

{4}-{5}-{6}	Square - Pentagon - Hexagon
{4}-{5}-{8}	Square - Pentagon - Octagon
{4}-{5}-{12}	Square - Pentagon - Dodecagon
{4}-{5}-{6/2}	Square - Pentagon - Hexagram
{4}-{6}-{7}	Square - Hexagon - Heptagon
{4}-{6}-{8}	Square - Hexagon - Octagon
{4}-{6}-{12}	Square - Hexagon - Dodecagon
{4}-{6}-{6/2}	Square - Hexagon - Hexagram
{4}-{8}-{12}	Square - Octagon - Dodecagon
{4}-{8}-{6/2}	Square - Octagon - Hexagram
{4}-{12}-{6/2}	Square - Dodecagon - Hexagram

{6}-{12}-{6/2}	Hexagon - Dodecagon - Hexagram

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

{5}
11,12	{6}
	12	{7}			{4}
12	10,11		{8}		{4}
12	11		11	{12}
					{5/2}
12	10		11	12		{6/2}
							{8/2}
								{12/2}

There is a very large number of possible three way dissections that can be performed. To limit this number I have restricted myself to looking for three way dissections of the regular polygons and polygrams that can be solved in twelve or fewer pieces.