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Strictly Convex Polytiles
The number of strictly convex p-tiles can be catalogued by brute force for
any finite even whole number p. The highest-sided strictly convex p-tile
is a regular p-gon.
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Tetratiles, Hexatiles and Octatiles
There only one tetratile, a square,
**1^4**. There are 3 hexatiles,
a regular hexagon, **1^6**, rhombus,
**1.2^2**, and an
equilateral triangle,
**2^3**. There are 4 octatiles:
a regular octagon, **1^8**, a
flat hexagon **1.1.2^2**,
a square, **2^4**, and a rhombus,
**1.3^2**.
Polytiles of the form **a.b^2 **are rhombi, alternating 2 angles.
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Decatiles
There are 7 convex decatiles, a regular decagon,
**1^10**, an octagon,
**2.1.1.1^2**, two hexagons:
**2.2.1^2** and
**3.1.1^2**, a regular pentagon,
**2^5**, and two rhombi:
**3.2^2**, and
**4.1^2**.
There is no special names for the irregular hexagons. The form **a.(1^c)^2
**, like **3.1.1^2 **might
be called a
polygonal-lens,
approximating 2 attached circular
arcs.
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Dodecatiles
There are 16 or 17 convex dodecatiles (depending whether chiral copies are
counted as 1 or 2): a regular dodecagon,
**1^12**, decagon
**2.1.1.1.1^2**, enneagon
**2.1.1^3**, 3 octagons
**2.1^4**,
**2.2.1.1^2**, and
**3.1.1.1^2**, a heptagon
**1.3.1.2.1.3.1**, 4
or 5 hexagons: **2^6**,
**3.1^3**,
**4.1.1^2**, and chiral pair
**1.2.3^2** and
**3.2.1**^2, one pentagon:
**4.1.3.3.1**, three
quadrilaterals (square)
**3^4**, (and rhombi)**
4.2^2**, and
**5.1^2**, and an equilateral
triangle **4^3**.
Polytiles of the form **a.b^n **are called isotoxal, having one edge type
withing its symmetry, and
2 vertex types which alternate.
The decagon
**2.1.1.1.1^2**
, octagon **3.1.1.1^2**,
and hexagon **4.1.1^2** can
be called polygonal-lens.
© 2020 Created by Tom Ruen |