This repository contains the ancillary material to the paper "Self-dual polyhedral cones and their slack matrices" by João Gouveia and Bruno F. Lourenço 
https://arxiv.org/abs/2207.11747

Contents:

1) Supports of slack matrices for strongly involutive self dual (sisd) cones:
supports_rank4.txt -> Contains the supports for matrices for all sisd 4-dim cones with 7 up to 15 extreme rays
supports_rank5.txt -> Contains the supports for matrices for all sisd 5-dim cones with 6 up to 9 extreme rays

2) Numerical psd slack matrices for self-dual polyhedral cones:
psd_slacks_rank4.txt-> Contains a psd slack matrix for all combinatorial types of self-dual 4-dim cone with 7 up to 15 extreme rays
psd_slacks_rank5.txt-> Contains a psd slack matrix for all combinatorial types of self-dual 5-dim cone with 6 up to 9 extreme rays

3) The main matlab functions that were used to create and manipulate these lists:
findpsdslack -> A function that given a support of a slack matrix that is symmetric and has non-zero diagonal searches for a psd realization of the slack matrix
issisd -> A function that given the support of a slack matrix verifies if the polytope is strongly independent self dual and if so, gives back a permuted matrix that is symmetric and has ones in the diagonal
generatesisd -> A function that generates the slack matrices of all 3-dimensional sisd polytopes, based on the work of Bracho et al.