The Foster cage is one of the four -cage graphs. Like the other -cages, the Foster cage has 30 nodes. It has 75 edges, diameter 3, girth 5, chromatic number 4, and is a quintic graph. Its LCF signature is , with the two order-15 LCF embeddings illustrated above with a number of other embeddings. None of the order-3 LCF embeddings have bilateral symmetry. A rotationally symmetric embedding consisting of three copies of a quartic graph with internal pentagram and external pentagon is also shown (E. Weisstein, Nov. 2, 2025).

The Foster cage is implemented in the Wolfram Language as GraphData["FosterCage"].

The automorphism group of the Foster cage has order 30.

The Foster cage satisfies the rhombus constraints and contains no known unit-distance forbidden subgraph, yet appears not to be a unit-distance. A number of embeddings found from different initial embeddings by minimizing the sum of square deviations from unit edge lengths until a local minimum was reached are illustrated above.