### There are 11 results

Broad Topics >

3D Geometry, Shape and Space > Tetrahedra

##### Age 11 to 14 Challenge Level:

Can you number the vertices, edges and faces of a tetrahedron so
that the number on each edge is the mean of the numbers on the
adjacent vertices and the mean of the numbers on the adjacent
faces?

##### Age 11 to 14 Challenge Level:

An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?

##### Age 11 to 14 Challenge Level:

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

##### Age 11 to 14 Challenge Level:

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

##### Age 14 to 16 Challenge Level:

Can you work out the dimensions of the three cubes?

##### Age 11 to 14 Challenge Level:

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

##### Age 14 to 16 Challenge Level:

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

##### Age 14 to 16 Challenge Level:

An irregular tetrahedron has two opposite sides the same length a
and the line joining their midpoints is perpendicular to these two
edges and is of length b. What is the volume of the tetrahedron?

##### Age 14 to 18

In this article, we look at solids constructed using symmetries of
their faces.

##### Age 7 to 16

A description of how to make the five Platonic solids out of paper.

##### Age 11 to 16 Challenge Level:

Toni Beardon has chosen this article introducing a rich area for
practical exploration and discovery in 3D geometry