We consider set systems that satisfy a certain octahedral parity property. Such systems arise when studying the colourful simplices formed by configurations of points of in R d ; configurations of low colourful simplicial depth correspond to systems with small cardinality. This construction can be used to find lower bounds computationally for the minimum colourful simplicial depth of a configuration, and, for a relaxed version of colourful depth, provide a simple proof of minimality.
['Grant Custard', 'Antoine Deza', 'Tamon Stephen', 'Feng Xie']
Small Octahedral Systems