Pyramid (geometry) in the context of Solid (geometry)

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 geometry, an apex (pl.: apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to refer to the vertex opposite from some "base". The word is derived from the Latin for 'summit, peak, tip, top, extreme end'. The term apex may be used in different contexts:

• In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side.

Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space).A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior.

Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms, cubes (and other polyhedrons), cylinders, cones (including truncated) and other solids of revolution.

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, a frustum (Latin for 'morsel'); (pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; otherwise, it is an oblique frustum.

The Großglockner (German: Großglockner [ˈɡroːsˌɡlɔknɐ] ), or just Glockner, is, at 3,798 metres above the Adriatic (12,461 ft), the highest mountain in Austria and highest mountain in the Alps east of the Brenner Pass. It is part of the larger Glockner Group of the Hohe Tauern range, situated along the main ridge of the Central Eastern Alps and the Alpine divide. The Pasterze, Austria's most extended glacier, lies on the Grossglockner's eastern slope.

The characteristic pyramid-shaped peak actually consists of two pinnacles, the Großglockner and the Kleinglockner (3,770 m or 12,370 ft, from German: groß 'big', klein 'small'), separated by the Glocknerscharte col.

Decoupage or découpage (/ˌdeɪkuːˈpɑːʒ/; French: [dekupaʒ]) is the art of decorating an object by gluing colored paper cutouts onto it in combination with special paint effects, gold leaf, and other decorative elements. Commonly, an object like a small box or an item of furniture is covered by cutouts from magazines or from purpose-manufactured papers. Each layer is sealed with varnishes (often multiple coats) until the "stuck on" appearance disappears and the result looks like painting or inlay work. The traditional technique used 30 to 40 layers of varnish which were then sanded to a polished finish.

Three dimensional decoupage (sometimes also referred to simply as decoupage) is the art of creating a three-dimensional (3D) image by cutting out elements of varying sizes from a series of identical images and layering them on top of each other, usually with adhesive foam spacers between each layer to give the image more depth. Pyramid decoupage (also called pyramage) is a process similar to 3D decoupage. In pyramid decoupage, a series of identical images are cut into progressively smaller, identical shapes which are layered and fixed with adhesive foam spacers to create a 3D "pyramid" effect.

In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face (but not on the same edge) as each other.

For example, a pyramid has no space diagonals, while a cube (shown at right) or more generally a parallelepiped has four space diagonals.

The Shard, also referred to as the Shard London Bridge and formerly London Bridge Tower, is a 72-storey mixed-use development supertall pyramid-shaped skyscraper, designed by the Italian architect Renzo Piano, in Southwark, London, that forms part of The Shard Quarter development. Standing 309.6 metres (1,016 feet) high, The Shard is the tallest building in the United Kingdom; the seventh-tallest building in Europe; the second-tallest outside Russia behind the Varso Tower in Warsaw, which beats the Shard by less than half a metre, and the 203rd tallest building in the world. The Shard replaced Southwark Towers, a 24-storey office block built on the site in 1975.

The Shard's construction began in March 2009; it was topped out on 30 March 2012 and inaugurated on 5 July 2012. Practical completion was achieved in November 2012. The tower's privately operated observation deck, The View from The Shard, was opened to the public on 1 February 2013. The glass-clad pyramidal tower has 72 habitable floors, with a viewing gallery and open-air observation deck on the 72nd floor, at a height of 244 metres (801 ft). The Shard was developed by Sellar Property Group on behalf of LBQ Ltd and is jointly owned by Sellar Property (5%) and the State of Qatar (95%).