Department of Computer Science, University of Oxford: Publication - Geometric characterization of the sporadic groups <span style="font-family: serif"><span style="font-family: serif;">Fi</span>22</span>‚ <span style="font-family: serif"><span style="font-family: serif;">Fi</span>23</span>‚ and <span style="font-family: serif"><span style="font-family: serif;">Fi</span>24</span>