# Kiteless Didoms

## Introduction

A *polydom* is a polyform
made up of diagonal half-domino shapes,
or 2×1 right triangles.
Here are some polydoms:

The term is due to Andrew Clarke.
The suffix -dom

is half the word domino

,
making it appropriate for a half-domino.

A *didom* is a polydom with two cells.
A short leg of one cell may be adjacent to a long leg of another, and
the long legs of two adjacent cells are allowed to overlap halfway.
Thus there are 13 different didoms:

The last didom is known as the kite. It is the only didom whose
vertices do not all lie on a common square grid.
This makes it awkward to use in didom tilings.
It must be used in pairs, as seen in Brendan Owen's
tiling of
a near-regular dodecagon with two sets of 13 didoms.
See Bernd Karl Rennhak's
Logelium
for more constructions using the kite didom.

Polydoms that do not contain kite didoms are called *kiteless*.
Below are various tilings with the kiteless didoms.

## Single Set

The 12 kiteless didoms can form any of three convex shapes:

All these shapes have multiple solutions—but none more than five.

## Double Set

A double set of kiteless didoms
can form two different rectangles or a square with a hole in the center:

It can also form a hexagon,
a rotary octagon,
and a decagon:

Besides these symmetric shapes, it can form these tridoms scaled up
by a factor of four.
Most of these tilings were found by Abaroth:

Abaroth also found this triangle with a hole …

… and many symmetric arrangements of the double
set of kiteless didoms.
You can download them in PDF format
[here] and
[here].

Last revised 2018-10-22.

Back to Polyform Tiling
< Polyform Curiosities

Col. George Sicherman
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