Other tags that relate to Which Solids Can We Make?
2D shapes and their properties. Regular polygons and circles. Polyhedra. Visualising. Practical Activity. Angle properties of polygons. Logo. Angles - points, lines and parallel lines. GeoGebra. Mathematical reasoning & proof.There are 22 results
Broad Topics > 3D Geometry, Shape and Space > Polyhedra
Which Solids Can We Make?
Age 11 to 14 Challenge Level:
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?
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.
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.
Paper Folding - Models of the Platonic Solids
Age 11 to 16
A description of how to make the five Platonic solids out of paper.
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 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?
Triangles to Tetrahedra
Age 11 to 14 Challenge Level:
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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?
Icosian Game
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.
Rhombicubocts
Age 11 to 14 Challenge Level:
Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices. . . .
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.
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
Tetrahedra Tester
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?
A Mean Tetrahedron
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?
Tetra Square
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.
Thinking 3D
Age 7 to 14
How can we as teachers begin to introduce 3D ideas to young children? Where do they start? How can we lay the foundations for a later enthusiasm for working in three dimensions?
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?
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.
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?
Investigating Solids with Face-transitivity
Age 14 to 18
In this article, we look at solids constructed using symmetries of their faces.
NRICH is part of the family of activities in the Millennium Mathematics Project.