
Truncating
the Platonic solids to create the Archimedean solids 
. 
Symmetrically truncating the vertices of the regular Platonic solids creates most 
. 
of the
semiregular Archimedean solids. This permits the symmetry of the latter to 
. 
be associated
with the former in a straightforward manner. For example the cube 
. 
and octahedron
can be progressively truncated to yield the cuboctahedron. The 
. 






Fig. 13a 
Fig. 13b 
Fig. 13c 
Fig. 13d 
Fig. 13e 
Truncated
cube 
Truncated 
Cuboctahedron 
Truncated 
Octahedron 
in a cube 
cube 

octahedron 

Required
parts 
8
large triangles 
8
triangles 
48 triangles 
8 triangles 
6
large squares 
6 squares 
6 squares 
12 pinges 
24
rectangles 
24 pinges 
84
pinges 

24
right triangles (48 for 13a) 



96
pinges (120 for 13a) 




. 
. 
. 
Fig. 13 
Truncating the cube and octahedron to make the cuboctahedron 
. 
truncated cube
and the truncated octahedron are generated in the process. Since 
. 
each vertex of
the polyhedra are symmetrically sliced off the resulting polyhedra 
retain the same
symmetry elements as the original. 
. 

Exercise: Truncating the vertices
of which polyhedron produces the triangle 

faces of the cuboctahedron? Which
one produces the square's? Why? 

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Geometry rules!  Symmetry association by truncation 