# List of Geometric Shapes

Welcome to the Math Salamanders' Geometric Shapes Information Page.

Here you will find a list of different geometric shapes to help you to identify a range of 2d and 3d shapes.

Along with each shape, we have also included the properties of each shape and other helpful information.

## 2d Geometric Shapes

Here are our list of 2d geometric shapes, including triangles, quadrilaterals and polygons

### List of Geometric Shapes - Triangles

 Equilateral Triangle Equilateral triangles have all angles equal to 60° and all sides equal length. All equilateral triangles have 3 lines of symmetry. Isoscles Triangle Isosceles triangles have 2 angles equal and 2 sides of equal length. All isosceles triangles have a line of symmetry. Scalene Triangle Scalene triangles have no angles equal, and no sides of equal length. Right Triangle Right triangles (or right angled triangles) have one right angle (equal to 90° ). Obtuse Triangle Obtuse triangles have one obtuse angle (an angle greater than 90° ). The other two angles are acute (less than 90° ). Acute Triangle Acute triangles have all angles acute.

### List of Geometric Shapes - Quadrilaterals

A quadrilateral is a polygon with 4 sides.

There are quite a few members of the quadrilateral family. There are also some members which are a subset of other members of this family!
See below if this confuses you!

 Square Squares have 4 equal sides and 4 right angles. They have 4 lines of symmetry. All squares belong to the rectangle family. All squares belong to the rhombus family. All squares are also parallelograms. Rectangle Rectangles have 4 sides and 4 right angles. They all have 2 lines of symmetry (4 lines if they are also a square!) All rectangles belong to the parallelogram family. Rhombus Rhombuses (rhombii) have 4 equal sides. Both pairs of opposite sides are parallel. They all have 2 lines of symmetry (4 lines if they are a square!) All rhombuses belong to the parallelogram family. Parallelogram Parallelograms have 2 pairs of parallel sides. Some parallelograms have lines of symmetry (depending on whether they are also squares, rectangles or rhombuses), but most do not. Trapezoid US (Trapezium UK) Trapezoids US (Trapeziums UK) have one pair of parallel sides. Some trapezoids have a line of symmetry. Please note the differences between the definitions for US and UK. Kite Kites have 2 pairs of equal sides which are adjacent to each other. Trapezium US (Trapezoid UK) Trapeziums US (Trapezoids UK) are quadrilaterals with no parallel sides. Please note the differences between the definitions for US and UK.

### Convex and Concave Polygons

Polygons can be concave or convex in their shape.

Convex shapes have all angles less than 180°

Concave shapes have at least one reflex angle greater than 180°

Triangles are always convex.

 Convex hexagon Convex shapes have no reflex angles (angles > 180° ) Concave hexagon Concave shapes have at least one reflex angle greater than 180° Convex pentagon Concave pentagon Convex octagon Concave octagon

### Regular and Irregular Polygons

Here is a list of regular polygons from 3 to 10 sides.

For each polygon, a regular and an irregular example have been shown.

Any regular shape will be mathematically similar to the example shown (having the same angles).

Regular shapes are always convex.

Irregular shapes can be concave or convex.

There are an infinite number of examples of different irregular polygons that could be shown, and only one example is given.

### IRREGULAR SHAPES

Equilateral Triangle

Sides: 3

Angle: 60°

Interior angles add up to 180°

Irregular Triangle

Square

Sides: 4

Angle: 90°

Interior angles add up to 360°

Pentagon

Sides: 5

Angle: 108°

Interior angles add up to 540°

Irregular Pentagon

Hexagon

Sides: 6

Angle: 120°

Interior angles add up to 720°

Irregular Hexagon

Heptagon

Sides: 7

Angle: 128.6° (to 1dp)

Interior angles add up to 900°

Irregular Heptagon

Octagon

Sides: 8

Angle: 135°

Interior angles add up to 1080°

Irregular Octagon

Nonagon

Sides: 9

Angle: 140°

Interior angles add up to 1260°

Irregular Nonagon

Decagon

Sides: 10

Angle: 144°

Interior angles add up to 1440°

Irregular Decagon

Hendecagon

Sides: 11

Angle: 147.3° (to 1dp)

Interior angles add up to 1620°

Irregular Hendecagon

Dodecagon

Sides: 12

Angle: 150°

Interior angles add up to 1800°

Irregular Dodecagon

#### Formula for Interior Angles of a Polygon

The formulae for the interior angles of a polygon are as follows:

Total of interior angles = 180 x (number of sides - 2)

Interior Angle of a regular polygon = total of interior angles / number of sides

### List of Geometric Shapes - Curved 2d Shapes

Here are some curved 2d shapes which have not yet been included.

 Circle Circles have a point in the centre from which each point on the diameter is equidistant. They have infinite lines of symmetry. How many sides does a circle have? This is an interesting question - the answer could be 0 (no straight sides), 1 curved side, or an infinite number of sides are all possible answers. Ellipse Ellipses are like circles which have been squashed or stretched. They have 2 lines of symmetry. They are also a special type of oval. The longest and shortest diameters of the ellipse are called the major and minor axes. These axes are also the lines of symmetry. Crescent Crescent shapes are made when two circles overlap, or when one circle is removed from another circle . The perimeter of crescents are made from two circular arcs. They have 1 line of symmetry. Our moon forms crescent shapes during its phases. Some countries such as Turkey or Algeria have crescent shapes on their flags.

## List of Geometrics Shapes - 3D Shapes

 Cube Cubes have 6 faces, 12 edges and 8 vertices. All sides on a cube are equal length. All faces are square in shape. A cube is a type of cuboid. Cuboid Cuboids have 6 faces, 12 edges and 8 vertices. All the faces on a cuboid are rectangular. Sphere Spheres have either 0 or 1 faces, 0 edges and 0 vertices. Ellipsoid Ellipsoids have either 0 or 1 faces, 0 edges and 0 vertices. Cylinder Cylinders have either 2 or 3 faces, 0 or 2 edges, and 0 vertices. Cone Cones have either 1 or 2 faces, 0 or 1 edges, and 1 apex (which is described by some mathematicians as a vertex). Triangular Prism Triangular Prisms have 5 faces, 9 edges, and 6 vertices. The two faces at either end are triangles, and the rest of the faces are rectangular. Hexagonal Prism Hexagonal Prisms have 8 faces, 18 edges, and 12 vertices. The two faces at either end are hexagons, and the rest of the faces are rectangular. Triangular-based Pyramid Triangular-based pyramids have 4 faces, 6 edges and 4 vertices. The base is a triangle. All of the faces are triangular. If the triangular faces making up the prism are all equilateral, then the shape is also called a Tetrahedron. Square-based Pyramid Square based pyramids have 5 faces, 8 edges and 5 vertices The base is a square. All the other faces are triangular. Hexagonal Pyramid Hexagonal pyramids have 7 faces, 12 edges, and 7 vertices. The base is a hexagon. All of the other faces are triangular.

### The 5 Platonic Solids

The platonic solids form a set of 5 polyhedra with the following special properties:

• the faces of the platonic solids have to be regular and congruent.
• the same number of faces meet at each vertex.
 Tetrahedron A Tetrahedrons is the same as a triangular pyramid. They have 4 triangular faces, 6 edges and 4 vertices. A regular tetrahedron has equilateral triangles for its faces, and is one of the 5 platonic solids. Cube (regular hexahedron) Cubes have 6 faces, 12 edges and 8 vertices. All sides on a cube are equal length. All faces are square in shape. A cube is a type of cuboid and is one of the 5 platonic solids. Octahedron Octahedrons are a shape with 8 faces, 12 edges and 6 vertices. A regular octahedron has equilateral triangles for its faces, and is one of the 5 platonic solids. Dodecahedron Dodecahedrons are a shape with 12 faces, 30 edges and 20 vertices. A regular dodecahedron has regular pentagons for its faces, and is one of the 5 platonic solids. Icosahedron Icosahedron are a shape with 20 faces, 30 edges and 12 vertices. All the faces are triangles. A regular icosahedron is one of the 5 platonic solids with all faces being equilateral triangles.

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