Resources tagged with: Polyhedra

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There are 22 results

Broad Topics > 3D Geometry, Shape and Space > Polyhedra

More Dicey Decisions

Age 16 to 18
Challenge Level

The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?

Tetra Inequalities

Age 16 to 18
Challenge Level

Prove that in every tetrahedron there is a vertex such that the three edges meeting there have lengths which could be the sides of a triangle.

Euler's Formula and Topology

Age 16 to 18

Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the. . . .

Classifying Solids Using Angle Deficiency

Age 11 to 16
Challenge Level

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

Proximity

Age 14 to 16
Challenge Level

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

Three Cubes

Age 14 to 16
Challenge Level

Can you work out the dimensions of the three cubes?

Investigating Solids with Face-transitivity

Age 14 to 18

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

Sliced

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?

Platonic and Archimedean Solids

Age 7 to 16
Challenge Level

In a recent workshop, students made these solids. Can you think of reasons why I might have grouped the solids in the way I have before taking the pictures?

Magnetic Personality

Age 7 to 16
Challenge Level

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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?

The Dodecahedron

Age 16 to 18
Challenge Level

What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?

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?

Platonic Planet

Age 14 to 16
Challenge Level

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

The Dodecahedron Explained

Age 16 to 18

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

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. . . .

Reach for Polydron

Age 16 to 18
Challenge Level

A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.

Modular Origami Polyhedra

Age 7 to 16
Challenge Level

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

Tetra Perp

Age 16 to 18
Challenge Level

Show that the edges AD and BC of a tetrahedron ABCD are mutually perpendicular when: AB²+CD² = AC²+BD².

Paper Folding - Models of the Platonic Solids

Age 11 to 16

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

Dodecawhat

Age 14 to 16
Challenge Level

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

Which Solid?

Age 7 to 16
Challenge Level

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.