1 CommentWednesday, 15 May 2019 | **Paul** We have just launched a new range called Crystal Polydron. The size of the pieces are the same as our Original Polydron, the shapes are all solid and are totally transparent. They look stunning on light tables and against a light source. The introduction of transparent pieces allows you to see inside the structure. |

Tuesday, 24 April 2018 | **Paul Stephenson** We use the same language to describe uniform tilings and polyhedra: *Platonic* if all the regular polygons are the same, *Archimedean* if there's a mixture, and a tiling - like the kagome pattern, 3.6.3.6 - can be thought of as an infinite polyhedron. What controls the size of the polyhedron is the *angular defect*, *d*, the difference from 360°, at each vertex. They total 720°, so, if there are *v* vertices, *vd* = 720°. |

Monday, 23 April 2018 | **Paul Stephenson** In the case of our own planet the story begins around 4.3 billion years ago with the appearance of solid matter: ions joining to form crystals. We have to jump forward the same amount of time before organic life had evolved with the sophistication to discover their structures. Right up until the middle of the twentieth century this evidence was still indirect: we observed the scattering pattern when samples were bombarded by X-rays. But the electron microscope and its successors enabled us to identify individual ions. An important two-dimensional pattern discovered among minerals is the subject of this piece. |

Tuesday, 4 July 2017 | **Paul Stephenson** To make a straight line, a 1-dimensional shape, we translate a point, a 0-dimensional shape. To make a square, a 2-dimensional shape, we translate the straight line perpendicular to itself. To make a cube, a 3-dimensional shape, we translate the square perpendicular to itself. |

Tuesday, 4 July 2017 | **Paul** In order to test out some challenge activities I went to a local High School to run the first activity with a lower ability Year 8 class. |

Tuesday, 30 May 2017 | **Paul Stephenson** An unmarked regular tetrahedron has planes of symmetry. It does not therefore have left- and right-handed forms. (The technical word for handedness is chirality.) But here are nets for two tetrahedra in which each face has a different colour. |

1 CommentMonday, 13 March 2017 | **Paul** As part of the London Schools Excellence Fund, The Compton School in partnership with Finchley Catholic High School recently held two maths masterclasses for strong Year 6 mathematicians from schools in the Barnet and Haringey areas. They were ably supported by Year 8 students from the The Compton and Year 9 students from Finchley Catholic. |

Tuesday, 14 February 2017 | **Paul Stephenson** Having built a polyhedron from a net or illustration, students will feel pleased with what they have done. But they can now capitalise on their success by finding the properties of their shape. Most important are the planes of mirror symmetry and axes of rotation symmetry. Then there is the matter of how many faces, edges and vertices they have. It is this second question which concerns us here. |

Tuesday, 14 February 2017 | **Paul Stephenson** Most Sudoku puzzles use the numbers 1 to 9, but you can use anything – letters, colours, shapes, …And you can make up puzzles with fewer items. We shall use just 4. If you think such puzzles are likely to be too simple, I warn you that we shall move from 'single' Sudoku to 'double' Sudoku and even 'triple double' Sudoku. |

Tuesday, 14 February 2017 | **Paul Stephenson** The 4 Colour Map Theorem says that you never need more than 4 colours to colour a map so that regions with the same colour don’t touch. You have to count the region round the edge because the theorem is really about a map drawn on a sphere. The theorem is shape-blind. It doesn’t matter what shape a region is. What matters are the regions it shares a border with. |