Vámos matroid

In mathematics, the Vámos matroid or Vámos cube is a matroid over a set of eight elements that cannot be represented as a matrix over any field.

It is named after English mathematician Peter Vámos, who first described it in an unpublished manuscript in 1968.

[1] The Vámos matroid has eight elements, which may be thought of as the eight vertices of a cube or cuboid.

The fifth circuit connects two opposite edges of the cuboid, each of which is shared by two of the chosen four faces.

Another way of describing the same structure is that it has two elements for each vertex of the diamond graph, and a four-element circuit for each edge of the diamond graph.