Catalan Solids
Starting with 
Taking the convex hull of 
End up with 
a regular tetrahedron 
four adjacent tetrahedra 
¡@
Starting with 
Taking the convex hull of 
End up with 
a regular dodecahedron 
an icosahedron and a dodecahedron 
¡@
Starting with 
Taking the convex hull of 
End up with 
A cube 
a cube and an octahedron 
¡@
Starting with 
Taking the convex hull of 
End up with 
a cube

a cube and an octahedron
¡@ 
¡@
Starting with 
Taking the convex hull of 
End up with 
an icosidodecahedron

an icosidodecahedron, a dodecahedron and an icosahedron

¡@
Starting with 
Taking the convex hull of 
End up with 
a regular octahedron

three octagons and a cube

¡@
Starting with 
Taking the convex hull of 
End up with 
a cuboctahedron 
a cuboctahedron, an octahedron and a cube 
¡@
Starting with 
Taking the convex hull of 
End up with 
an icosidodecahedron 
an icosidodecahedron, an icosahedron and a dodecahedron 
¡@
Starting with 
Taking the convex hull of 
End up with 
an octahedron 
an octahedron and a cube 
¡@
Starting with 
Taking the convex hull of 
End up with 
a dodecahedron 
an icosahedron and a dodecahedron 
¡@
Starting with 
Taking the convex hull of 
End up with 
a dodecahedron 
an icosahedron and a dodecahedron 
References: Eugene Charles Catalan Rhombic Triacontahedron