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La Ora Stelo (the golden star), dedicated to Jean-Pierre Puisais-Hée, is a puzzle whose pieces are polymultiforms (more precisely polyores).
The polyores are polymultiforms obtained by juxtaposition of several triangles as the 2 triangles below :
These 2 triangles are isoceles : their sides measure respectively 1, 1 and
for the first and 1,
and
for the second.
is the golden number (the golden ratio, the
golden proportion) :
These 2 triangles are called "golden triangles" (someones speaks about "golden triangle" for the second and "golden gnomon" for
the first).
Their angles measure respectively 36°, 36° et 108° for the first and 72°, 72° et 36° for the second.
But what really matters is that, if we take the area of the first as unit area (so its area is 1), the area of the second is
.
The polyores below are arranged in order of area (their area is red pointed) :
The 32 polyores above are the 32 pieces of La Ora Stelo.
They cover area of 42
+ 42 ; if we add 5 little triangles, we obtain area of 44
+ 43 : it's the area of a regular pentagon with side
+ 4.
The first goal of this puzzle is to realize a golden star by 22 of its pieces. Here is a possible weft for this star which have
area 36
+
22 :
There is a vast number of possible wefts ( to see an example of transformation of the weft, click here ).
I have not solution and I don't know if one exists.
(solution of Robin King)
pentagons, diamonds, trapeziums, stars, decagons, kites, "dunce's caps", "mushrooms", "darts", "witche's hats", "diaboloes", "pantaloons", "shirts", "fans", "flowers", hexagons, "tents", parallelograms, triangles, "wheels", "cooking-pots", "mountains", "norias", "butterflies", "foxes", "barrels", "apple trees", "crowns", and so on ...
