Four Way Dissections

Author : Gavin Theobald

{3}-{4}-{6}-{8} Triangle — Square — Hexagon — Octagon
{3}-{4}-{6}-{12} Triangle — Square — Hexagon — Dodecagon
{3}-{4}-{6}-{6/2} Triangle — Square — Hexagon — Hexagram
{3}-{4}-{8}-{6/2}  Triangle — Square — Octagon — Hexagram

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

Triangle - Square - Hexagon - Octagon

Triangle — Square — Hexagon — Octagon (18 pieces)

Triangle - Square - Hexagon - Octagon

Triangle — Square — Hexagon — Octagon (17 pieces with 2 turned over)

 Triangle - Square - Hexagon - Dodecagon

Triangle — Square — Hexagon — Dodecagon (17 pieces with 4 turned over)

 Triangle - Square - Hexagon - Hexagram

Triangle — Square — Hexagon — Hexagram (16 pieces)

 Triangle - Square - Octagon - Hexagram

Triangle — Square — Octagon — Hexagram (16 pieces)

Triangle - Square - Octagon - Hexagram

Triangle — Square — Octagon — Hexagram (15 pieces with 2 turned over)