Abraham Sharp's Polyhedra
Abraham Sharp (1651-1742) was an astronomer at the English Royal Observatory.
He wrote a book, Geometry Improv'd, published in 1718, rich in novel
polyhedra, especially ones with tetragonal faces. The book shows how to
cut these new solids from cubes of wood. Plate II of the book gives
a flavor of the complexity of the polyhedra and the necessary cuts:
The most complex of these has 120 faces. What is most amazing is
that Sharp calculates all the necessary dimensions for constructing these
solids with fifteen to twenty decimal places of accuracy! Here is
a typical section of his text:
For three reasons, I list him here as an artist
of polyhedra. Firstly, the solids which he constructed are of no
special mathematical value; they are not models of anything other than
themselves. They are purely aesthetic objects, geometric sculptures
which he is sharing with us so we can enjoy their forms. Secondly,
the plates are "neatly engraved by his own hands". (Imperial Encyclopedia,
1812, "Sharp, Abraham".) And thirdly, as an astronomer, he well knew
that there was no earthly reason to work out this many significant digits.
It is far beyond what is needed or usable in construction. He clearly
wrote this book out of a love for the beauty of geometry.