Assertion: dodecahedron's face | /r/CapableOf | meet at each vertex
Facets:
Source sentences:
text: It has five equilateral triangular faces meeting at each vertex.
text: Thus, just as hexagons have angles not less than 120° and cannot be used as the faces of a convex regular polyhedron because such a construction would not meet the requirement that at least three faces meet at a vertex and leave a positive defect for folding in three dimensions, icosahedra cannot be used as the cells of a convex regular polychoron because, similarly, at least three cells must meet at an edge and leave a positive defect for folding in four dimensions (in general for a convex polytope in n dimensions
text: The convex regular icosahedron is usually referred to simply as the regular icosahedron, one of the five regular Platonic solids, and is represented by its Schläfli symbol {3, 5}, containing 20 triangular faces, with 5 faces meeting around each vertex.
text: (since regular polygons must have three or more faces); n ≥ 3 n \geq 3 n ≥ 3 (since at least three faces must meet at any vertex or it would be flat).
text: Three faces meet at each vertex.
text: Since three faces meet at each vertex it has 20 × 9 / 3 = 60 vertices (these are the outermost layer of visible vertices and form the tips of the "spines") and 20 × 9 / 2 = 90 edges (each edge of the star polyhedron includes and connects two of the 180 visible edges).
text: Three faces meet at each vertex.
text: The factor of 3 in the triangular and hexagonal sections seems a little out of place, except that we have three faces meeting at each vertex.
text: Three faces meet at each vertex.
text: Three faces meet at each vertex.
text: Four faces meet at each vertex.
text: Three faces meet at each vertex.
text: Five faces meet at each vertex.
text: n n n is the number of faces that meet at a vertex.
text: Thus, just as hexagons have angles not less than 120° and cannot be used as the faces of a convex regular polyhedron because such a construction would not meet the requirement that at least three faces meet at a vertex and leave a positive defect for folding in three dimensions, icosahedra cannot be used as the cells of a convex regular polychoron because, similarly, at least three cells must meet at an edge and leave a positive defect for folding in four dimensions (in general for a convex polytope in $ n $ dimensions
text: The convex regular icosahedron is usually referred to simply as the regular icosahedron, one of the five regular Platonic solids, and is represented by its Schläfli symbol {3, 5}, containing 20 triangular faces, with 5 faces meeting around each vertex.
text: The convex regular icosahedron is usually referred to simply as the regular icosahedron, one of the five regular Platonic solids, and is represented by its Schläfli symbol {3, 5}, containing 20 triangular faces, with 5 faces meeting around each vertex.