(Isoperimetric polygons)

When I was child the square was the polygon with four equal edges.

PolyEdges(3x1+3xSQR5) Puzzle

I define a series of polygons by their edges, on a squared grid. For example below there are the 5 possible polygons with perimeter = 2+2SQR(5).


Here there are the possible polyedges with perimeter = 3+3sqr(5). We could name them:



The IsoPeriploes(3+3SQR5) are triangles, quadrilaterals, pentagons or hexagons. Their area is always integer of 2, 3, 4, 5 or 6. It is possible to define many other PolyEdges.

The pieces have a good capability of aggregation (but it isn't trivial!):

PolyEdges puzzle

Not all IsoPeriploes(3+3SQR5) tile the plane, but someone do it with fantasy:

PolyEdges tiling

Isoperimetric Polyominoes

Order 4, 6, 8 Isoperimetric polyominoes


Order 10 Isoperimetric polyominoes

Order 12 Isoperimetric Polyominoes

It's better to define the pieces below as Order 12 Isoperimetric Polyominoes because as IsoPeriploes(12) there are pieces on squared grid which remember us the Pitagora's theorem.

Order 12 Isoperimetric polyominoes

With these 25 pieces you could compose a 10x15 rectangle. You could see other constructions on the Andrew Clarke Polyominoes pages.

Order 12 Isoperimetric polyominoes Rectangle

You must add these 9 pieces to obtain the complete series of IsoPeriploes(12) on squared grid. It's also possible to compose a trapezium with all the 34 pieces.

IsoPeriploes(12) Puzzle



WARNING: the page is experimental, the sets could be incomplete, the puzzles not solvable.


First edition: 16 June 2000 - Last revision: 21 June 2000



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