# What shape has no line of symmetry and rotational symmetry order 3?

For example the triskelion (the three legs) on the Isle of Man flag.

### How do you sketch a figure with rotational symmetry but no line symmetry?

When a shape is rotated about its centre, if it comes to rest in a position and looks exactly like the original, then it has rotational symmetry. A shape like an equilateral triangle would therefore have an order of rotational symmetry of 3. The general rule for a regular polygon (shapes such as pentagons, heptagons, octagons etc. is, that the number of sides is the same as the number of lines of symmetry, which is…

### Which type of symmetry is displayed?

"Displayed" is not a type of symmetry. There are two types of symmetry: Reflectional (or mirror) in which a line can be placed on a shape in such a way that if the shape was folded along that line the two halves would match exactly. For example the letter W has a line of symmetry that runs vertically down its middle which allows the two halves to be folded onto each other to form a…

### Which shape has line of symmetry but not rotational symmetry?

There are infinitely many such shapes: Take any odd-sided regular polygon Move one vertex away from the side opposite it in a perpendicular direction any distance you like. The resulting shape has one line of symmetry (from the vertex moved to the centre of the opposite side) and no rotational symmetry. Done to an equilateral triangle (a regular "3-agon") this creates an isosceles triangle.

### What is the difference between line symmetry and rotational symmetry?

Line or reflective symmetry is really a special case of rotational symmetry but from a different viewpoint. In line symmetry imagine a line going north to south on the page. If you rotate an image out of the page around that line through 180 degrees you get a reflection. For rotational symmetry imagine that same line being perpendicular to the page so that you see it as a dot. The image is then rotated around…