Polyhedra

There are 45 NRICH Mathematical resources connected to Polyhedra

problem

Guess what?

Age

7 to 11

Challenge level

Can you find out which 3D shape your partner has chosen before they work out your shape?

problem

Three cubes

Age

14 to 16

Challenge level

Can you work out the dimensions of the three cubes?

problem

Pythagoras for a tetrahedron

Age

16 to 18

Challenge level

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.

problem

Tetra perp

Age

16 to 18

Challenge level

Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.

problem

Cut nets

Age

7 to 11

Challenge level

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

problem

Tet-trouble

Age

14 to 16

Challenge level

Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

problem

Shadow play

Age

5 to 7

Challenge level

Here are shadows of some 3D shapes. What shapes could have made them?

problem

Octa-flower

Age

16 to 18

Challenge level

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?

problem

Next size up

Age

7 to 11

Challenge level

The challenge for you is to make a string of six (or more!) graded cubes.

problem

Skeleton shapes

Age

5 to 7

Challenge level

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?