Apex (geometry) in the context of Square pyramid

A pyramid (from Ancient Greek πυραμίς (puramís) 'pyramid', from the Egyptian pir-em-us, the vertical height of the structure.) is a structure whose visible surfaces are triangular in broad outline and converge toward the top, making the appearance roughly a pyramid in the geometric sense. The base of a pyramid can be of any polygon shape, such as triangular or quadrilateral, and its surface-lines either filled or stepped.

A pyramid has the majority of its mass closer to the ground with less mass towards the pyramidion at the apex. This is due to the gradual decrease in the cross-sectional area along the vertical axis with increasing elevation. This offers a weight distribution that allowed early civilizations to create monumental structures.

In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In particular, axial precession can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.

Earth's precession was historically called the precession of the equinoxes, because the equinoxes moved westward along the ecliptic relative to the fixed stars, opposite to the yearly motion of the Sun along the ecliptic. Historically, the discovery of the precession of the equinoxes is usually attributed in the West to the 2nd-century-BC astronomer Hipparchus. With improvements in the ability to calculate the gravitational force between planets during the first half of the nineteenth century, it was recognized that the ecliptic itself moved slightly, which was named planetary precession, as early as 1863, while the dominant component was named lunisolar precession. Their combination was named general precession, instead of precession of the equinoxes.

A pyramid is a polyhedron (a geometric figure) formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. A pyramid is a conic solid with a polygonal base. Many types of pyramids can be found by determining the shape of bases, either by based on a regular polygon (regular pyramids) or by cutting off the apex (truncated pyramid). It can be generalized into higher dimensions, known as hyperpyramid. All pyramids are self-dual.

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called vertices, are zero-dimensional points while the sides connecting them, also called edges, are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between the base and apex is the height. The area of a triangle equals one-half the product of height and base length.

In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated within a unique flat plane. More generally, four points in three-dimensional Euclidean space determine a solid figure called tetrahedron.

In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called the apex or vertex.

A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base. In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, it extends infinitely far. In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a double cone. Each of the two halves of a double cone split at the apex is called a nappe.

A finial (from Latin finis 'end') or hip-knob is an element marking the top or end of some object, often formed to be a decorative feature.

In architecture, it is a small decorative device, employed to emphasize the apex of a dome, spire, tower, roof, or gable or any of various distinctive ornaments at the top, end, or corner of a building or structure. A finial is typically carved in stone. Where there are several such elements they may be called pinnacles. The very top of a finial can be a floral or foliated element called a bouquet.

In geometry, bisection is the division of something into two equal or congruent parts (having the same shape and size). Usually it involves a bisecting line, also called a bisector. The most often considered types of bisectors are the segment bisector, a line that passes through the midpoint of a given segment, and the angle bisector, a line that passes through the apex of an angle (that divides it into two equal angles).In three-dimensional space, bisection is usually done by a bisecting plane, also called the bisector.

In a hierarchy or tree structure of any kind, a superior is an individual or position at a higher level in the hierarchy than another (a "subordinate" or "inferior"), and thus closer to the apex.

In geometry, a hyperpyramid is a generalisation of the normal pyramid to n dimensions.

In the case of the pyramid one connects all vertices of the base (a polygon in a plane) to a point outside the plane, which is the peak. The pyramid's height is the distance of the peak from the plane. This construction gets generalised to n dimensions. The base becomes a (n – 1)-polytope in a (n – 1)-dimensional hyperplane. A point called apex is located outside the hyperplane and gets connected to all the vertices of the polytope and the distance of the apex from the hyperplane is called height. This construct is called a n-dimensional hyperpyramid.

In geometry, a base is a side of a polygon or a face of a polyhedron, particularly one oriented perpendicular to the direction in which height is measured, or on what is considered to be the "bottom" of the figure. This term is commonly applied in plane geometry to triangles, parallelograms, trapezoids, and in solid geometry to cylinders, cones, pyramids, parallelepipeds, prisms, and frustums.

The side or point opposite the base is often called the apex or summit of the shape.

In geometry, an altitude of a triangle is a line segment through a given vertex (called apex) and perpendicular to a line containing the side or edge opposite the apex. This (finite) edge and (infinite) line extension are called, respectively, the base and extended base of the altitude. The point at the intersection of the extended base and the altitude is called the foot of the altitude. The length of the altitude, often simply called "the altitude" or "height", symbol h, is the distance between the foot and the apex. The process of drawing the altitude from a vertex to the foot is known as dropping the altitude at that vertex. It is a special case of orthogonal projection.

Altitudes can be used in the computation of the area of a triangle: one-half of the product of an altitude's length and its base's length (symbol b) equals the triangle's area: A=hb/2. Thus, the longest altitude is perpendicular to the shortest side of the triangle. The altitudes are also related to the sides of the triangle through the trigonometric functions.

In geometry, a cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces; it has eight vertices and twelve edges. A rectangular cuboid (sometimes also called a "cuboid") has all right angles and equal opposite rectangular faces. Etymologically, "cuboid" means "like a cube", in the sense of a convex solid which can be transformed into a cube (by adjusting the lengths of its edges and the angles between its adjacent faces). A cuboid is a convex polyhedron whose polyhedral graph is the same as that of a cube.

General cuboids have many different types. When all of the rectangular cuboid's edges are equal in length, it results in a cube, with six square faces and adjacent faces meeting at right angles. Along with the rectangular cuboids, parallelepiped is a cuboid with six parallelogram faces. Rhombohedron is a cuboid with six rhombus faces. A square frustum is a frustum with a square base, but the rest of its faces are quadrilaterals; the square frustum is formed by truncating the apex of a square pyramid.In attempting to classify cuboids by their symmetries, Robertson (1983) found that there were at least 22 different cases, "of which only about half are familiar in the shapes of everyday objects".

A keystone (or capstone) is the wedge-shaped stone at the apex of a masonry arch or typically round-shaped one at the apex of a vault. In both cases it is the final piece placed during construction and locks all the stones into position, allowing the arch or vault to bear weight. In arches and vaults (such as quasi-domes) keystones are often enlarged beyond the structural requirements and decorated. A variant in domes and crowning vaults is a lantern. A portion of the arch surrounding the keystone is called a crown.

Keystones or their suggested form are sometimes placed for decorative effect in the centre of the flat top of doors, recesses and windows, so as to form an upward projection of a lintel, as a hallmark of strength or good architecture.