Modified decagon

I created a new shape from Paul Bourke’s concave decagon (third in from left). You can view it here… http://paulbourke.net/geometry/tilingplane/

A selection of periodic tilings below.

There are various ways to string tiles together to form three types of ‘slip planes’. These can be used as building blocks in some situations. The first example (zigzag) includes reflections.

Wavy (low profile). I have found six unique configurations (reflections not shown).

Wavy (high profile). Seven unique configurations (reflections not shown).

Central cores change when combining different configurations of slip-planes.

Grouping of decagons can produce ever expanding ‘motifs’, which can produce some interesting formations.

A single decagon can completely surround itself in various different ways.

The group of decagons on the left produce a ‘sunflower’. A maximum of five adjacent ‘petals’ can be used in a pattern. Two groups of four are also possible.

The thick black line or ‘handlebar’ indicates where a choice can be made. For example, by positioning a decagon (third from the left) another ‘handlebar’ forms. Placing of single decagons thereafter, are more likely to become forced.

The decagons at the heart of this pattern display mirror symmetry. All other decagons placed outside of this are forced.

This impressive double pentagon star tessellation utilises all five decagon rotations and their mirrors.

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