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.
