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In geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
, the elongated square pyramid is one of the Johnson solids (). As the name suggests, it can be constructed by elongating a square pyramid () by attaching a cube to its square base. Like any elongated pyramid
A pyramid (from el, πυραμίς ') is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilat ...
, it is topologically (but not geometrically) self- dual.
Formulae
The following formulae for theheight
Height is measure of vertical distance, either vertical extent (how "tall" something or someone is) or vertical position (how "high" a point is).
For example, "The height of that building is 50 m" or "The height of an airplane in-flight is ab ...
(), surface area () and volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...
() can be used if all faces are regular, with edge length :
:
:
:
Dual polyhedron
The dual of the elongated square pyramid has 9 faces: 4 triangular, 1 square and 4 trapezoidal.Related polyhedra and honeycombs
The elongated square pyramid can form atessellation of space
In geometry, a honeycomb is a ''space filling'' or '' close packing'' of polyhedral or higher-dimensional ''cells'', so that there are no gaps. It is an example of the more general mathematical ''tiling'' or ''tessellation'' in any number of dim ...
with tetrahedra
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
, similar to a modified tetrahedral-octahedral honeycomb
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2.
Other names i ...
.
See also
* Elongated square bipyramidReferences
External links
* {{Polyhedron-stub Johnson solids Self-dual polyhedra Pyramids and bipyramids