Assertion: icosahedron's face | /r/CapableOf | meet at each vertex
Facets:
value: in the case of the icosahedron
type: OTHER
value: in the icosahedron
type: LOCATION
value: together
type: MANNER
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: It haes five triangular faces meetin at 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.
text: f f is a 1 / 3 1/3 turn around the center of a face touching that 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: The icosahedron also has five triangular faces that join together at each vertex.
text: In the icosahedron, five faces meet at every 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: It has five triangular faces meeting 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: Furthermore, in order to qualify as one of the platonic solids, the shape must have the same number of faces meeting at each vertex, and the dihedral angle between any two faces must be the same.
text: At each vertex or corner at least three faces or more must meet.
text: We also know that p>2 and q>2, since each face must have at least 3 sides, and at least 3 faces must meet 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: Five faces meet at each vertex.
text: In the case of the icosahedron, five faces meet at each vertex.
text: The faces are congruent, regular polygons with the same number of faces meeting at each vertex (corner).
text: The twenty triangular faces have five 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: 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: n n n is the number of faces that meet at a vertex.
text: It haes five triangular faces meetin at 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.