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Vertex of a solid

Vertex Ver"tex, n.; pl. Vertexes, L. Vertices. [L. vertex, -icis, a whirl, top of the head, top, summit, from vertere to turn. See Verse, and cf. Vortex.] A turning point; the principal or highest point; top; summit; crown; apex. Specifically: (a) (Anat.) The top, or crown, of the head. (b) (Anat.) The zenith, or the point of the heavens directly overhead. (c) (Math.) The point in any figure opposite to, and farthest from, the base; the terminating point of some particular line or lines in a figure or a curve; the top, or the point opposite the base. Note: The principal vertex of a conic section is, in the parabola, the vertex of the axis of the curve: in the ellipse, either extremity of either axis, but usually the left-hand vertex of the transverse axis; in the hyperbola, either vertex, but usually the right-hand vertex of the transverse axis. Vertex of a curve (Math.), the point in which the axis of the curve intersects it. Vertex of an angle (Math.), the point in which the sides of the angle meet. Vertex of a solid, or of a surface of revolution (Math.), the point in which the axis pierces the surface.

Vertex Ver"tex, n.; pl. Vertexes, L. Vertices. [L. vertex, -icis, a whirl, top of the head, top, summit, from vertere to turn. See Verse, and cf. Vortex.] A turning point; the principal or highest point; top; summit; crown; apex. Specifically: (a) (Anat.) The top, or crown, of the head. (b) (Anat.) The zenith, or the point of the heavens directly overhead. (c) (Math.) The point in any figure opposite to, and farthest from, the base; the terminating point of some particular line or lines in a figure or a curve; the top, or the point opposite the base. Note: The principal vertex of a conic section is, in the parabola, the vertex of the axis of the curve: in the ellipse, either extremity of either axis, but usually the left-hand vertex of the transverse axis; in the hyperbola, either vertex, but usually the right-hand vertex of the transverse axis. Vertex of a curve (Math.), the point in which the axis of the curve intersects it. Vertex of an angle (Math.), the point in which the sides of the angle meet. Vertex of a solid, or of a surface of revolution (Math.), the point in which the axis pierces the surface.

- same number of faces meeting at each vertex. Five solids meet these criteria: Geometers have studied the Platonic solids for thousands of years. They...

- are symmetric to each other: A global isometry of the entire solid takes one vertex to the other while laying the solid directly on its initial position...

- Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular...

- There are 13 related Johnson solids, 5 by diminishment, and 8 including gyrations: The rhombicosidodecahedron shares its vertex arrangement with three nonconvex...

- any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has...

- In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the...

- geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges. Every edge has exactly two faces, and every vertex is surrounded...

- each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also...

- a vertex configuration is a shorthand notation for representing the vertex figure of a polyhedron or tiling as the sequence of faces around a vertex....

- In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners...

- are symmetric to each other: A global isometry of the entire solid takes one vertex to the other while laying the solid directly on its initial position...

- Platonic solids and Archimedean solids, the faces of Catalan solids are not regular polygons. However, the vertex figures of Catalan solids are regular...

- There are 13 related Johnson solids, 5 by diminishment, and 8 including gyrations: The rhombicosidodecahedron shares its vertex arrangement with three nonconvex...

- any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has...

- In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the...

- geometry, a polyhedron is a solid in three dimensions with flat faces and straight edges. Every edge has exactly two faces, and every vertex is surrounded...

- each separating a triangle from a square. As such, it is a quasiregular polyhedron, i.e. an Archimedean solid that is not only vertex-transitive but also...

- a vertex configuration is a shorthand notation for representing the vertex figure of a polyhedron or tiling as the sequence of faces around a vertex....

- In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners...

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