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Take a cube of side length one unit. A vertex of the cube and the centres of the three faces not containing that vertex form the vertices of a tetrahedron. What is the surface area of this tetrahedron?
Find the shape and symmetries of the two pieces of this cut cube.
The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?