Polyhedra

There are 45 NRICH Mathematical resources connected to Polyhedra
Guess What?
problem
Favourite

Guess what?

Age
7 to 11
Challenge level
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Can you find out which 3D shape your partner has chosen before they work out your shape?
Shadow Play
problem
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Shadow play

Age
5 to 7
Challenge level
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Here are shadows of some 3D shapes. What shapes could have made them?

Octa-flower
problem
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Octa-flower

Age
16 to 18
Challenge level
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Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?
Next size up
problem
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Next size up

Age
7 to 11
Challenge level
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The challenge for you is to make a string of six (or more!) graded cubes.

Skeleton Shapes
problem
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Skeleton shapes

Age
5 to 7
Challenge level
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How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

Which solid?
problem
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Which solid?

Age
7 to 16
Challenge level
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This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
Triangles to Tetrahedra
problem
Favourite

Triangles to tetrahedra

Age
11 to 14
Challenge level
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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Which solids can we make?
problem
Favourite

Which solids can we make?

Age
11 to 14
Challenge level
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Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Three cubes
problem
Favourite

Three cubes

Age
14 to 16
Challenge level
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Can you work out the dimensions of the three cubes?
Pythagoras for a Tetrahedron
problem
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Pythagoras for a tetrahedron

Age
16 to 18
Challenge level
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In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation of Pythagoras' Theorem.