Euler's formula. Convex Polyhedra

Properties of 3D shapes

Understand and use Euler's formula to connect the number of vertices, faces and edges of 3D shapes

• Sphere

• Cone

• Cylinder

Non-Polyhedra

• Cube

• Hexagonal Prism

• Octahedron

Polyhedra

Polyhedra - 3D shape, characterised by the fact that all its faces are flat.

Multiple Choice

Which one is polyhedron?

• Cone

• Sphere

• Ellipsoid

• Tetrahedron

Multiple Choice

Which one is non-polyhedron?

• Cone

• Square-based pyramid

• Icosahedron

• Hexagonal Prism

Parts of a polyhedron

Multiple Choice

Question again =)

Who is principal of our School?

• mr. Fuad

• mr. Akbar

• mr. Artur

• mr. Gurban

V + F - E = 2

V - vertices
F - faces
E - edges

Euler's Formula

Multiple Choice

V + F - E = 2

Find the number of edges in polyhedra with the following properties:

6 vertices and 5 faces

• 7

• 8

• 9

• 10

Multiple Choice

V + F - E = 2

Find the number of edges in polyhedra with the following properties:

10 vertices and 7 faces

• 13

• 14

• 15

• 16

Multiple Choice

An octahedron has 8 faces and 12 edges. How many vertices does it have?

• 18

• 10

• 6

• 2

Multiple Choice

An icosahedron has 30 edges and 12 vertices. How many faces does it have?

• 14

• 16

• 18

• 20

Multiple Choice

A dodecahedron has 12 faces and 20 vertices. How many edges does it have?

• 30

• 32

• 34

• 36

Multiple Choice

A tetrahedron has 4 faces and 4 vertices. How many edges does it have?

• 4

• 6

• 8

• 10

Multiple Choice

A polyhedron has 12 vertices and 30 edges. How many faces does it have?

• 14

• 16

• 18

• 20

Multiple Choice

A polyhedron has 6 vertices and 8 faces. How many edges does it have?

• 12

• 14

• 16

• 18

Multiple Choice

A solid has 13 vertices and 24 edges.

Given that Euler's Formula applies, how many faces does it have?

• 12

• 13

• 14

• 15

For polygons with 3 through 12 sides

3 - tri
4 - tetra
5 - penta
6 - hexa
7 - hepta
8 - octa
9 - nona
10 -deca
11 - undeca
12 - dodeca

Multiple Choice

Penta

• 4

• 5

• 6

• 7

Multiple Choice

Octa

• 6

• 7

• 8

• 9

Euler's formula does not work for every type of polyhedron. All the polyhedra so far have been examples of convex polyhedra!

A line joining any two vertices falls completely on or within the shape itself

Convex polyhedron

A line joining any two vertices falls completely on or within the shape itself

Convex polyhedron

Convex polyhedron

A line joining any two vertices falls completely on or within the shape itself

Poll

Do you understand everything?

• Yes

• No