Dissections of a square to an arithmetic series of polygons

Author : Gavin Theobald

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{3} Triangle
{3}+{4} Triangle + Square
{3}+{4}+{5} Triangle + Square + Pentagon
{3}+{4}+{5}+{6} Triangle + Square + Pentagon + Hexagon
{3}+{4}+{5}+{6}+{7} Triangle + Square + Pentagon + Hexagon + Heptagon
{3}+{4}+{5}+{6}+{7}+{8}  Triangle + Square + Pentagon + Hexagon + Heptagon + Octagon
 
{4} Square
{4}+{5} Square + Pentagon
{4}+{5}+{6} Square + Pentagon + Hexagon
{4}+{5}+{6}+{7} Square + Pentagon + Hexagon + Heptagon
{4}+{5}+{6}+{7}+{8} Square + Pentagon + Hexagon + Heptagon + Octagon
 
{4} Square
{4}+{6} Square + Hexagon
{4}+{6}+{8} Square + Hexagon + Octagon
{4}+{6}+{8}+{10} Square + Hexagon + Octagon + Decagon
{4}+{6}+{8}+{10}+{12} Square + Hexagon + Octagon + Decagon + Dodecagon
 
{4} Square
{4}+{7} Square + Heptagon
{4}+{7}+{10} Square + Heptagon + Decagon
 
{4} Square
{4}+{8} Square + Octagon
{4}+{8}+{12} Square + Octagon + Dodecagon
{4}+{8}+{12}+{16} Square + Octagon + Dodecagon + Hexadecagon
 
{6} Hexagon
{6}+{8} Hexagon + Octagon
{6}+{8}+{10} Hexagon + Octagon + Decagon
{6}+{8}+{10}+{12} Hexagon + Octagon + Decagon + Dodecagon

Triangle Triangle + Square Triangle + Square + Pentagon Triangle + Square + Pentagon + Hexagon Triangle + Square + Pentagon + Hexagon + Heptagon Triangle + Square + Pentagon + Hexagon + Heptagon + Octagon

Square — Triangle (4 pieces)

Square — Triangle + Square (6 pieces)

Square — Triangle + Square + Pentagon (11 pieces)

Square — Triangle + Square + Pentagon + Hexagon (13 pieces)

Square — Triangle + Square + Pentagon + Hexagon + Heptagon (19 pieces)

Square — Triangle + Square + Pentagon + Hexagon + Heptagon + Octagon (27 pieces)

Square Square + Pentagon Square + Pentagon + Hexagon Square + Pentagon + Hexagon + Heptagon Square + Pentagon + Hexagon + Heptagon + Octagon

Square — Square (1 piece)

Square — Square + Pentagon (7 pieces)

Square — Square + Pentagon + Hexagon (12 pieces)

Square — Square + Pentagon + Hexagon + Heptagon (17 pieces)

Square — Square + Pentagon + Hexagon + Heptagon + Octagon (21 pieces)

Square Square + Hexagon Square + Hexagon + Octagon Square + Hexagon + Octagon + Decagon Square + Hexagon + Octagon + Decagon + Dodecagon

Square — Square (1 piece)

Square — Square + Hexagon (7 pieces)

Square — Square + Hexagon + Octagon (13 pieces)

Square — Square + Hexagon + Octagon + Decagon (16 pieces)

Square — Square + Hexagon + Octagon + Decagon + Dodecagon (25 pieces)

Square Square + Heptagon Square + Heptagon + Decagon

Square — Square (1 piece)

Square — Square + Heptagon (9 pieces)

Square — Square + Heptagon + Decagon (14 pieces)

Square Square + Octagon Square + Octagon + Dodecagon Square + Octagon + Dodecagon + Hexadecagon

Square — Square (1 piece)

Square — Square + Octagon (8 pieces)

Square — Square + Octagon + Dodecagon (14 pieces)

Square — Square + Octagon + Dodecagon + Hexadecagon (20 pieces)

Hexagon Hexagon + Octagon Hexagon + Octagon + Decagon Hexagon + Octagon + Decagon + Dodecagon

Square — Hexagon (5 pieces)

Square — Hexagon + Octagon (10 pieces)

Square — Hexagon + Octagon + Decagon (17 pieces)

Square — Hexagon + Octagon + Decagon + Dodecagon (20 pieces)

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