A history of Greek mathematics - Wilbourhall.org

ON SEMI-REGULAR' POLYHEDRA 101
similar procedure with the icosahedron and dodecahedron
produces P n and P l2
(see Figs. 3, 4 for the case of the icosahedron).
Fig. 3. Fig. 4.
The two remaining solids P 10
, P 13
cannot be so simply produced.
They are represented in Figs. 5, 6, which I have
Fig. 5. Fig. 6.
taken from Kepler. P l0
is the snub cube in which each
solid angle is formed by the angles of four equilateral triangles
and one square; P 13
is the snub dodecahedron, each solid
angle of which is formed by the angles of four equilateral
triangles and one regular pentagon.
We are indebted to Arabian tradition for
(y)
The Liber Assumptorum.
Of the theorems contained in this collection many are
so elegant as to
afford a presumption that they may really
be due to Archimedes. In three of them the figure appears
which was called dpftrjXos, a shoemaker's knife, consisting of
three semicircles with a common diameter as shown in the
annexed figure. If N be the point at which the diameters