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An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap with the top truncated, and so it corresponds to a spherical frustum. The surface of the spherical segment (excluding the bases) is called spherical zone. Geometric parameters for spherical ...
The upper bound for the density of a strictly jammed sphere packing with any set of radii is 1 – an example of such a packing of spheres is the Apollonian sphere packing. The lower bound for such a sphere packing is 0 – an example is the Dionysian sphere packing. [27]
A solid angle in the form of a right circular cone can be projected onto a sphere, defining a spherical cap where the cone intersects the sphere. The magnitude of the solid angle expressed in steradians is defined as the quotient of the surface area of the spherical cap and the square of the sphere's radius.
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
Dually, if v is a vertex of P, then there is a cone that has its apex at v and that is tangent to O in a circle; this circle forms the boundary of a spherical cap within which the sphere's surface is visible from the vertex. That is, the circle is the horizon of the midsphere, as viewed from the vertex. The circles formed in this way are ...
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In geometry, a spherical sector, [1] also known as a spherical cone, [2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap.