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?
Sandy from The Mount School, York, sent these nets for the
solids and Jacqui from the same school sent similar nets. Each
solid is made up of 18 squares and 8 equilateral triangles with 3
squares and a triangle around each vertex.
Sandy found that each solid has 48 edges, 24 vertices and 26
faces. It remains a Tough Nut Challenge to describe the differences
between these two solids in terms of their planes of symmetry and
axes of rotational symmetry.
To help with this you need a model. At the Mount School they use
a method that is quick and easy for making models as this classroom
picture shows (though it is not of rhombicubocts). The tabs slot
together and you need to make the tabs narrow so they don't cover
up much of the faces of the solid.
Alternatively you could use Polydron to make the models, or a
similar construction kit with plastic pieces that clip together.
With equipment of this sort you can make models quickly and use
your time to concentrate on the mathematics.