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In Math, a 3-D (solid) shape made by fitting polygons together is called a polyhedron. You have already met some polyhedra, e.g. cuboids. A regular polyhedron is formed from regular polygons all the same size and shape.

1.

Which of these shapes is not a polyhedron?

Cube

Pyramid

Sphere

Triangular prism

Polyhedra have straight edges and flat surfaces

2.

The polygons forming the surface of a polyhedron are called .......

areas

edges

faces

sides

3.

Where the straight sides of two polygons meet on the surface of a polyhedron they form a(n) .......

area

edge

line

side

4.

The place on the surface of a polygon where several edges meet is called a .......

corner

dent

point

vertex

5.

What is the name of the regular polyhedron in which four equilateral triangles meet at each vertex?

Hexahedron

Icosahedron

Octahedron

Tetrahedron

Imagine two square-based pyramids stuck together

6.

If you add the number of faces of a polyhedron to the number of its vertices the result is always .......

equal to the number of edges

2 more than the number of edges

2 less than the number of edges

1 more than the number of edges

V + F = E + 2 is a formula discovered by the Swiss mathematician Leonhard Euler

7.

How many edges has a pyramid with a hexagonal base?

6

8

10

12

Use Euler's formula with F = 7 and V = 7

8.

How many faces has the regular polyhedron made with pentagons?

5

10

12

15

This is called a dodecahedron

9.

A polyhedron with four rectangles or squares meeting at each vertex is called .......

a cuboid

a parallelepiped

a trapezoid

impossible

When four right angles meet at a point they completely fill the flat space so they cannot be folded into a solid

10.

A polyhedron formed from rectangles set at right-angles to a polygonal base and top is called a .......

parallel

prism

prune

pyramid

The cross section of a prism is the same shape and size along its whole length