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Abstract polytope
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===Rank 1: the line segment=== [[Image:An Edge (Line Segment) and its Hasse Diagram.PNG|thumb|240px|The graph (left) and Hasse Diagram of a line segment]] There is only one polytope of rank 1, which is the line segment. It has a least face, just two 0-faces and a greatest face, for example {ΓΈ, '''a, b, ab'''}. It follows that the vertices '''a''' and '''b''' have rank 0, and that the greatest face '''ab''', and therefore the poset, both have rank 1.
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