ON SEMI-REGULAR POLYHEDRA 
101 
a that, accord- 
1 already been 
)e his method, 
regular solids 
r solids. We 
ag off angles 
lie cube, P 2 by 
m the faces ; 
es, and P 3 by 
5 icosahedron, 
:agons, in the 
ng pentagons, 
cutting off all 
parallel to the 
rst the cube, 
is which leave 
dicular to the 
a the corners 
beral triangles 
scting all the 
off from the 
leave in each 
in it has its 
h each edge is 
e Fig. 2) ; this 
the edges and 
,. An exactly 
similar procedure with the icosahedron and dodecahedron 
produces P n and P x2 (see Figs. 3, 4 for the case of the icosa 
hedron). 
The two remaining solids P l0 , P X3 cannot be so simply pro 
duced. They are represented in Figs. 5, 6, which 1 have 
taken from Kepler. _f[ 0 is the snub cube in which each 
solid angle is formed by the angles of four equilateral triangles 
and one square; P Vi 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 dpftgXoy, 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