Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3 cube?
60 pieces and a challenge. What can you make and how many of the
pieces can you use creating skeleton polyhedra?
A very mathematical light - what can you see?
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. Each has a band of 8 squares around
the 'equator' and two square faces at the top and bottom (parallel
to the equator) containing the 'north and south poles' at their
centres. Draw the net for making each of the shapes and make the
models for yourself either with card or a plastic constriction kit.
How many faces, edges and vertices does each solid have? How many
planes of symmetry and how many axes of rotational symmetry?
The solid on the left is one of the classical semi-regular or
Archimedean solids but the one on the right was almost
entirely ignored until it was made known by JCP Miller in the
1930s. Perhaps people thought the two were the same - can you
describe the differences?