Assertion: polyhedron's face | /r/CapableOf | meet at edge
Facets:
value: together
type: MANNER
Source sentences:
text: John Skilling discovered an overlooked degenerate example, by relaxing the condition that only two faces may meet at an edge.
text: It is clear that a set of polygons that form the pattern of a closed convex polygon satisfies the following conditions: (1) exactly two faces meet at each edge and three or more faces meet at each vertex; (2) the number of vertices, faces, and edges satisfies Euler’s condition; (3) we can go from a polygon to any other polygon by way of adjacent polygons; (4) the sides common to two polygons have equal length; and (5) the sum of the plane angles of the faces at a common vertex is less than 277.
text: First we note that since two faces meet in one edge, we must have
text: Along each edge exactly two faces come together, so an edge corresponds to exactly two sides: the total number of sides is 2E.
text: — two faces meet along each one of these edges.
text: Adjacent faces meet at edges, and edges meet at vertices.
text: One further nonconvex degenerate polyhedron is the great disnub dirhombidodecahedron, also known as Skilling's figure, which is vertex-uniform, but has pairs of edges which coincide in space such that four faces meet at some edges.
text: It is clear that a set of polygons that form the pattern of a closed convex polygon satisfies the following conditions: (1) exactly two faces meet at each edge and three or more faces meet at each vertex; (2) the number of vertices, faces, and edges satisfies Euler’s condition; (3) we can go from a polygon to any other polygon by way of adjacent polygons; (4) the sides common to two polygons have equal length; and (5) the sum of the plane angles of the faces at a common vertex is less than 277.
text: It is clear that a set of polygons that form the pattern of a closed convex polygon satisfies the following conditions: (1) exactly two faces meet at each edge and three or more faces meet at each vertex; (2) the number of vertices, faces, and edges satisfies Euler’s condition; (3) we can go from a polygon to any other polygon by way of adjacent polygons; (4) the sides common to two polygons have equal length; and (5) the sum of the plane angles of the faces at a common vertex is less than 277.