Inconcievable Symmetries (artwork)
Inconcievable Symmetries Condoms, 16 in 2014

This form is based on the small rhombicosidodecahedron, an Archimedean solid with 120 edges. The underlying polyhedral edges have been replaced by pairs of packed condoms connected at their corners with split-pin fasteners.

Background and Inspiration

The box of condoms.

I had been exploring polyhedral-related forms one could make using squares. Being a parent of then college-aged children one is always surprised by what one finds lying around the house. For some time I noticed a box in the dining room and finally asked my wife what was in it. Condoms! she exclaimed in a somewhat exasperated manner. I thought, perhaps out loud, What are we going to do with roughly 1000 red, yellow, and green condoms? Well, when life gives you lemons, you make lemonade. Condoms? Art!

The construction of this piece starts with the Small Rhombicosidodecahedron, one of the Archimedean solids; these polyhedra have regular polygonal faces (equal angles and edge lengths) and their vertices all lie on the surface of a circumscribing sphere. By replacing each edge with a square, the polyhedra's vertices become openings as do the faces. In this case, the triangular faces pop out on the otherwise spherical form.

Small Rhombicosidodecahedron

The underlying icosahedral symmetry, which is shared by many viruses, allowed me to build this in modules. Twelve red pentagonal units and twenty yellow triangular units. Green condoms were used on the inside to help obscure the packaging. While initially rigid, the stiffness of the packaging in relation to the weight eventually caused some sagging. I created a dodecahedron frame using wooden dowels connected with a 3D printed vertex as a support scaffolding.

This was one of the my pieces included in the In the Realm of Forms exhibit in 2015. Below are two additional pictures from that exhibition.

Inconceivable Symmetries, gallery photo from the exhibition In the Realm of Forms.
Inconceivable Symmetries, detail.

I included a picture of this piece in a talk I gave at the Bridge conference in 2015. Writer Siobhan Roberts was in the audience and included an anecdote on this piece in her article Cogito, Ergo Summer.

Related Works

Publication History

  • Nonplanar expansions of polyhedral edges in Platonic and Archimedean solids, Bridges Conference Proceedings, July 2015. Paper (pdf)

Exhibition History

  • In the Realm of Forms, Pearl Conard Art Gallery, The Ohio State University at Mansfield. 9 November – 8 December 2015.


  • Cogito, Ergo Summer by Siobhan Roberts. The New Yorker. 27 August 2015.
  • Nonplanar expansions of polyhedral edges in Platonic and Archimedean solids, Bridges Conference Proceedings, July 2015. Paper (pdf)