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 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.
