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Abstract polytope
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, an abstract polytope is an algebraic <a href="/facts/Partially_ordered_set/qb4a3FAX">partially ordered set</a> which captures the dyadic property of a traditional <a href="/facts/Polytope/a76nXrL0">polytope</a> without specifying purely geometric properties such as points and lines. </p><p>A geometric <a href="/facts/Polytope/a76nXrL0">polytope</a> is said to be a <i>realization</i> of an abstract polytope in some real <a href="/facts/N-dimensional_space/0ktmUyac">N-dimensional space</a>, typically <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean</a>. This abstract definition allows more general <a href="/facts/Combinatorics/k14xUoKT">combinatorial</a> structures than traditional definitions of a polytope, thus allowing new objects that have no counterpart in traditional theory. </p>