POLYHEDRON MODELS (Part one)

The back of Flint Court E2 has long been home to a remarkable set of polyhedron models.

These were constructed by Michael Longuet-Higgins (Coll 1939-43), assisted by his brother Christopher and by Freeman Dyson (both Coll, 1937-41), two years above him in College.

The collection splits naturally into three groups, and this note concerns the models on the left hand side of the cabinet: the platonic solids and (some of) their stellations.

Stellation

To explain what is meant by a stellation it helps to drop down into two dimensions as a warm up. Figure 1 in the gallery shows a regular heptagon: 7 evenly spaced points round a circle with adjacent points connected by line segments. However, if rather than simply drawing line segments we draw entire lines connecting these points, we obtain the richer figure 2.

Embedded within this we see the first and second stellations of the heptagon: symmetrical regions of the plane defined by the lines that surround the original heptagon (figures 3 & 4).

Moving back up to three dimensions we can play exactly the same game with regular (or Platonic) polyhedra. If we extend the 12 planes that form the faces of a regular dodecahedron (Image 5) we obtain the three possible stellations shown beside it in image 6.

If we move up from the dodecahedron to the 20-sided icosahedron, the number of possibilities explodes. Image 8 shows some of the simpler possible stellations. 

In 1938 Coxeter et al published a book entitled The Fifty-Nine Icosahedra, which enumerated possible stellations, and it seems plausible that this book prompted Michael to begin the models project. As a young academic Michael would go on to collaborate with Coxeter on another polyhedron project (of which more in a future issue). The Winchester collection contains only a selection of the possible stellated icosahedra and it remains a mystery how Michael chose which to include and which to omit.

However, it is no surprise that the crown jewel of the display, housed separately as it will not fit on the shelves, is the largest, or final, stellation (image 9).