Exploring Frameworks - Polydron

Written by Bob Ansell

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This publication is designed to show what can be achieved withPolydron and Polydron Frameworks.

Polydron materials have been widely used in education and inthe home for over 30 years and have enriched the experiencesof many thousands of children.

Indeed, for many children Polydron and Polydron Frameworkshave given them access to the wonderful world of 3-D geometryand construction.

Bob AnsellBob Ansell is a Senior Lecturer in Mathematics Educationat the University of Northampton. He has written andproduced many publications that support teachers,students and parents to explore the potential of Polydronand Polydron Frameworks.

Copyright © Bob Ansell

1 Just Four Triangles

■ Polydron has fourdifferent shapedtriangles.

■ Here is a different tetrahedronyou can make.

■ Make an unusual tetrahedronwith these four triangles.

■ Select four small equilateraltriangles to make a tetrahedron.

■ Make a collection of as many different tetrahedrons(tetrahedra) as you can.


2 Pyramids

■ Make this square-basedpyramid. It has smallequilateral triangles for thesloping faces.

■ Make an unusualsquare-based pyramidwith these pieces.

■ This is a hexagonalbased pyramid withisosceles triangles forthe sloping sides.

■ A triangular-based pyramid is alsocalled a tetrahedron. Here is anenlarged one made from fourtriangles of each colour.


3 Prisms

■ This prism has small equilateraltriangles for the end faces.

■ This prism looks similar to the oneabove but has large equilateraltriangles for the end faces.

■ Prisms may have any polygonfor the end faces and a beltof squares or rectangles.

■ This cube is a special prism.


4 Antiprisms

■ Antiprisms are wonderfulsolids that have a polygon forthe top and bottom and a beltof triangles.

■ Unlike a prism, an antiprismhas no plane of symmetryparallel to its end faces.

■ Can you see why this octahedronis a special antiprism?


5

■ Pentominoes are arrangements of fivesquares.

■ Find as many pentominoes as youcan.

■ Some pentominoes can be folded tomake an open box.

■ Decide which of the pentominoesbelow will make an open box and havea blue square for the base.

■ There are twelve different pentominoes.Can you find them all?

Pentominoes


5

■ Pentominoes are arrangements of fivesquares.

■ Find as many pentominoes as youcan.

■ Some pentominoes can be folded tomake an open box.

■ Decide which of the pentominoesbelow will make an open box and havea blue square for the base.

■ There are twelve different pentominoes.Can you find them all?

Pentominoes


■ Take six squares and make acube.

■ Check that the the two bluesquares are on oppositefaces of the cube.

■ Which of these three arrangementsare nets of a cube?

■ Can you find all eleven nets of a cube?

6 Nets of a Cube


7

■ There are five Platonic Solids, named after the Greekphilosopher, Plato.

■ Platonic Solids each contain only one sort ofregular polygon. At every vertex you will seethe same arrangement of polygons.

■ This tetrahedron has four equilateraltriangles, with three meeting at each vertex.

■ The cube has six squares with threemeeting at each vertex.

■ The octahedron below has eight triangleswith four meeting at each vertex.

■ The dodecahedron needstwelve regular pentagons.

■ The icosahedron has twenty equilateraltriangles with five meeting at each vertex.

Platonic Solids

See the Platonic Solids video at polydron.co.uk/videos


■ Archimedean Solids are named after the Sicilianmathematician and engineer, Archimedes.

■ These solids are made from more than onesort of regular polygon, but every vertex isthe same.

■ Here are some of the thirteen differentArchimedean Solids.

■ Most of those above have symmetry. But thefinal one on the right, called the snub cube, hasno symmetry, making it tricky to construct.

8 Archimedean Solids


9

■ The funny house below has been made from parts of thetwo smaller two solids. Can you see how it was done?

■ This funny house has an octagonfor a base.

■ Make it taller or join two together.

■ Can you make it taller?

■ Make this funny house with large trianglesand rectangles.

■ The funny house below has been createdfrom part of an icosahedron andthen adding a strange top.

Funny Houses

What will you make?

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Exploring Frameworks - Polydron