Icosahedral and cuboctahedral arrangements of calixarenes, a nanometer-scale, spheroidal assembly of 12 calixarene molecules, can be manipulated in a highly controlled fashion. Previously, such assemblies were observed to favor placement of the calixarenes at the vertexes of an icosahedron. A supramolecular constraint is employed in order to enforce molecular alignment and produce a cuboctahedral arrangement. The internal volume of the cuboctahedron is approximately 30% greater than that of the icosahedron. Furthermore, in stark contrast to that of the icosahedral Platonic solid, the shell of the cuboctahedral Archimedean solid is porous.