The Foster cage is one of the four 
-cage graphs. Like the other
-cages,
the Foster cage has 30 nodes. It has 75 edges,
graph diameter 3, girth
5, chromatic number 4, and is a quintic
graph. Its LCF notation signature is 
, with the two order-15 LCF drawings illustrated
above with a number of other drawings. None of the order-3 LCF drawings have bilateral
symmetry. A rotationally symmetric drawing
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 forbidden subgraph for unit-distance embeddings, yet appears not to be a unit-distance graph. A number of drawings found from different initial drawings by minimizing the sum of squared deviations from unit edge lengths until a local minimum was reached are illustrated above.
