Assertion: polyhedron | /r/HasProperty | convex
Facets:
value: based on (a
type: OTHER
Source sentences:
text: A polyhedron is said to be convex if it lies entirely on one side of any plane containing one of its faces; then the faces are also convex.
text: A polyhedron is called a convex one, if all its diagonals are placed inside of it.
text: A polyhedron is said to be convex if it lies entirely on one side of any plane containing one of its faces; then the faces are also convex.
text: A polyhedron is convex if all its diagonals are inside or on its surface.
text: A polyhedron is said to be convex if its surface (comprising its faces, edges and vertices) does not intersect itself and the line segment joining any two points of the polyhedron is contained in the interior and surface.
text: If the figure be entirely to one side of any face the polyhedron is said to be " convex, " and it is obvious that the faces enwrap the centre once; if, on the other hand, the figure is to both sides of every face it is said to be concave, " and the centre is multiply enwrapped by the faces.
text: Furthermore, we know polyhedron is convex based on (a).
text: It turns out that, as long as your polyhedron is convex (has no sticky out bits) and has no holes running through it, the number of vertices minus the number of edges plus the number of faces,
text: According to Euler’s theorem, if the polyhedron is convex or is homeomorphic to a convex polyhedron, then its Euler characteristic is 2.
text: A polyhedron is said to be convex if it lies entirely on one side of any plane containing one of its faces; then the faces are also convex.