Shoveler update

I didn’t realise at the time but a shoveler can be cut from a enneamond.  The waste produces another shape which I have called a coot.  Further cuts produce a cygnet (more on this later perhaps).

Shoveler, coot & cygnet

Shoveler, coot & cygnet2

 

The shoveler and coot in combination can produce a regular hexagon.   Other permutations are possible.

 

It is interesting to note that the shoveler has 8 sides, the coot 7 and the cygnet 9.

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Shoveler Motifs

Michael Dowle has redrawn his original findings of the new shape.  Most of the angles are rudimentary but the others are quite odd.

Shoveler diagram - Michael Doyle2

 

I have since found a couple of motifs that can be tiled periodically.  The coloured double hexes help to show how it was constructed.

 

Here’s another…

 

A combination of the two (with one modification) produces something like this…

Shoveler-motif4

The Shoveler

The new shape has been dubbed the ‘Shoveler’ as it resembles a duck on water.  I missed off a couple of internal angles (D) last time round.  The two examples on the right show that B+C+D=360 and A+D=360 (creating a double hex).

 

Here are a few more ‘seeds’…

Octag-seed20

 

Next up is a few small periodic/radial tilings.  I coloured in the double hexes in the bottom right image, to show the chaotic nature of the pattern.

 

New shape – seeds

Following on from the previous post, the new shape (below) can be thought of as ‘parts’ (A, B and C) to aid pattern making.

Octag-seed0

 

Below are some of the combinations that could be used as starting points for possibly much larger tilings.

 

Here’s a few more…

 

I still have others to show but have run out of time.

Transformed heptiamond

This particular heptiamond can produce an unlimited array of interesting patterns.

 

Furthermore, by placing three in a particular arrangement, a new shape emerges (currently unnamed).

Octag-heptiamondOctag-heptiamond2

 

However, there were a couple of angles that I could not determine, so I asked the help of Michael Dowle who very kindly came up with the answers.

Dave186e

Drawing by Michael Dowle

 

Disappointingly, initial experimentation with the new shape, didn’t seem to work for radial/chaotic tiling.  As you can see below, the shape (highlighted in green), doesn’t quite fit in two of the examples and the other is miles out!

 

Curiously though and to my surprise, I have since discovered many ways that the new shape can tile, seemingly very chaotically.  Results of this coming soon…