The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
The diagram shows a regular pentagon with sides of unit length.
Find all the angles in the diagram. Prove that the quadrilateral
shown in red is a rhombus.
ABCDE is a regular pentagon of side length one unit. BC produced
meets ED produced at F. Show that triangle CDF is congruent to
triangle EDB. Find the length of BE.
Fold R and S up to the centre line EO, so that they meet to form a straight line and make a pentagon.
If you make 12 pentagons in this way and assemble them, using your 'flaps' and 'pockets', you can make a dodecahedron.
A4 paper has sides in the ratio$\sqrt2$ to $1$.
If you use A4 paper for this construction and try to make regular pentagons there is a small error in the angle at E. Find this error and find the dimensions of the paper which you would need to use to get an accurate regular pentagon and hence an accurate regular dodecahedron.
1) You can construct other platonic solids using paper and this article explains how.
2) Have a look at the October 2000 Article titled Classifying Solids using Angle Deficiency
3) You can download a demo version of Stella , a computer program which lets you create and view polyhedra on the screen, then print out the nets required to build your own models out of paper. Small Stella and Great Stella are available from the Stella Website.
4) Alternatively, print out the models from this pdf available at the British Crystallographic Association's Website