The Fourth PlinthThe Fourth PlinthPolyhedral Life

Theme:The OlympicsTask:Design a sculpture linked to the Olympics using polyhedra.

Background:The fourth plinth in Trafalgar Square is an empty pedestal that has been empty since 1841.Over the past number of years there has been a changing exhibition of different sculptures on it, including Anthony Gormley's "The One and the Other". Over 100 days, members of the public stood on the plinth 24 hours a day.

Your structure needs to take the place of the

cowboy picture

What dimensions does it need to be?

Here are a selection of polyhedra you

may wish to consider in your planning

Cube

Hexagonal prism

Pentagonal prism

Triangular prism

Octagonal prism

Cuboid

Cylinder

Materials

When you make your model/sculpture, you can choose to construct it from a wide variety of materials. These may include the following:

• Carving of wood, stone, plaster and cement• Welding of metal (steel and copper) plates• Twisting and wrapping of wire• Modeling of forms in clay, wax and plaster• Casting of bronze, steel and plastic• Working in iron and copper• Blowing or moulding of glass

The following slide shows examples of statues made from different materials to give you an idea of the finish and aesthetic qualities of your model/statue.

Copper

Bronze

Marble Sheet Metal

Glass

Iron

Granite

Sheet Metal

PerspexExamples of how

different materials are used to create sculptures

Costs

In the table below are the costs of a selection of materials, from which you may choose to make your model/statue. They have been split into whether you need to calculate the volume or the surface area

VOLUME SURFACE AREA

Copper £3 per Kg(Density of Copper is 8930 kg/cubic metre)

Marble £59.50 + VAT per square metre

Iron £4 per Kg(Density of Iron is 7850 kg/cubic metre)

Granite £25 + VAT per square metre

Bronze £3.65 per Kg(Density of Bronze is 8430 kg/cubic metre)

Sheet Metal £11.25 per square metre

Perspex £7.88 per square metre

Glass £23.50 per square metre

N.B. Where the cost has been given in terms of weight (i.e per Kg), you will need to use the density of the material in your calculations.

Chosen material is Chosen material is

Total volume =Remember that you will need to submit additional calculations

to support this

Total surface area =Remember that you will need to submit additional calculations

to support this

Cost of statue =Remember that you will need to submit evidence of how you

have costed your statue

Cost of statue =Remember that you will need to submit evidence of how you

have costed your statue

Please include any additional information or costings here

Please include any additional information or costings here

Please affix a photographof your model here Title of Submission:

Submitted by:

Materials to be used:Estimated amount of material required:(please provide calculations on a separate sheet)

Estimated cost of structure:

Please provide an explanation of the vision/story behind your choice of structure:

Fourth Plinth Submission

Formulae you may need to knowArea of:• Rectangle = length × width• Triangle = 1/2 base × height

• Circle = πr²• Trapezium = 1/2 (a + b) × vertical height

(where a and b are the two parallel sides)• Surface area of sphere = 4 πr²

Volume of:• Cuboid = length × width × height• Prism = area of cross-section × height• Cylinder = πr² h• Cone = 1/3 πr² h

• Pyramid = 1/3 × base area × height

• Sphere = 4/3 πr²

To find the surface area of a shape, find the area of each face and add them

together.

Enlarging your design to estimate materials needed and cost

To be able to estimate the quantity of materials needed and the costing involved, you first need to be able to work out the

enlarged dimensions.

General Rule

• If the lengths in a shape or solid are all multiplied by a scale factor of k, then the areas will be multiplied by a scale factor of k² and the volumes will be multiplied by a scale factor of k³.

• For example, if the lengths are enlarged with scale factor 4, then the areas will be enlarged with scale factor 16 and the volumes will be enlarged with scale factor 64.

Plan of action• Draw a sketch of the sculpture you would like to make• What polyhedra could you use to create your sculpture?• How much paper, card or other material will you need?

What other resources will you require?• Split the project up into individual tasks within your group

and decide who is responsible for each task• Work out how much it will cost to make your sculpture using

the costing sheet• Complete the submission form to bid for your sculpture to

appear on the plinth

Dodecahedron IcosidodecahedronTetrahedron

CubeOctahedron

Icosahedron Hexagonal prism

Pentagonal prism

Triangular prism

Octagonal prism

Cuboctahedron

Square based pyramid

Cuboid

Cylinder

Here are a selection of polyhedra you

may wish to consider in your planning

Cone

Sphere

Pyramids and ConesVolume = 1/3 x area of base x height

Other polyhedra and spheres

A few semi-regular polyhedra