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ALL OF THE SHAPES IN THIS IMAGE ARE RHOMBI (another word for “rhombusses”) BUT ONLY THOSE LABELLED 2 ARE DIAMONDS.

In the image: shape number 1 (purple) is a **Square **(not a diamond), because it is a **quadrilateral** (4 sides) with four $90^{\circ}$ **right-angles**. The fact that it is “turned around and balanced on a corner” does not change the fact that it’s a square. Non-mathematicians will often say this is a “diamond” because it’s balanced on a corner. But it’s not a diamond: it’s a square!

**DIAMOND:** The shapes labelled number 2 (blue, red, green) are all **Diamonds**, because they are each made up of two equilateral (all sides the same length) triangles stuck together. I’ve emphasised this by drawing a dotted line between the two equilateral triangles in the blue diamond.

Notice how the three diamonds if we squished them together would form a regular hexagon – which is of course made up of six equilateral triangles placed together.

**POLYIAMONDS:** A Diamond is a special type of **Polyiamond **(“many triangles”) – the collective name for shapes made up of one or more equilateral triangles stuck together base to base. If you wanted to you could say that a single equilateral triangle is a **moniamond **(one triangle). The sequence then goes **diamond **(two triangles), **triamond **(three), **tetriamond **(4), **pentiamond **(5) and so on. There are 3, 4, 12 different types of Tetriamond, Pentiamond, Hexiamond because of the different ways in which you can stick 4, 5, 6 triangles together, and it’s fun to try to sketch them all: have a go!

**RHOMBUS (“wonky square”):** The shapes labelled number 3 are both **rhombi**, because they are quadrilaterals whose four sides are all equal in length. The same is true for all the shapes 1, 2 and 3, so they are all rhombi, but only 1 is a square and only 2 are diamonds.

**SUMMARY:** All Diamonds are Rhombi, but not all Rhombi are Diamonds.

For more on strange shapes, see here for some non-squares that are all pretending to be squares !!

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