Trisha Shetty (Editor)

Square pyramid

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Type
  
JohnsonJ92 – J1 – J2

Schläfli symbol
  
( ) ∨ {4}

Rotation group
  
C4, [4], (44)

Volume
  
1/3 × l² × h

Number of faces
  
5

Base shape
  
Square

Vertex configuration
  
4(3.4)(3)

Symmetry group
  
C4v, [4], (*44)

Dual polyhedron
  
self

Number of edges
  
8

Number of vertices
  
5

Square pyramid Square Pyramid Images of Shapes

Surface area
  
a × (1 + 2 ×√((a/2)² + h²)

Shapes with similar faces
  
Cube, Cuboid, Triangular prism

Pyramid how to draw a square pyramid


In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.

Contents

Square pyramid Square pyramid Wikipedia

Square pyramid part 1


Johnson solid (J1)

Square pyramid Square Pyramid Clipart Clipart Kid

If the sides are all equilateral triangles, the pyramid is one of the Johnson solids (J1). The 92 Johnson solids were named and described by Norman Johnson in 1966.

Square pyramid httpsuploadwikimediaorgwikipediacommons55

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.

Square pyramid Spinning Square Pyramid

The Johnson square pyramid can be characterized by a single edge-length parameter a. The height H (from the midpoint of the square to the apex), the surface area A (including all five faces), and the volume V of such a pyramid are:

Square pyramid Square Pyramid Clipart Clipart Kid
H = 1 2 a A = ( 1 + 3 ) a 2 V = 2 6 a 3 .

Other square pyramids

Other square pyramids have isosceles triangle sides.

For square pyramids in general, with base length l and height h, the surface area and volume are:

Square pyramid Square Pyramid Definition amp Properties Video amp Lesson Transcript
A = l 2 + l l 2 + ( 2 h ) 2 V = 1 3 l 2 h .

Square pyramids fill space with tetrahedra, truncated cubes or cuboctahedra.

Dual polyhedron

Square pyramid Square Pyramid Definition amp Properties Video amp Lesson Transcript

The square pyramid is topologically a self-dual polyhedron. The dual edge lengths are different due to the polar reciprocation.

Topology

Like all pyramids, the square pyramid is self-dual, having the same number of vertices as faces.

A square pyramid can be represented by the Wheel graph W5.

References

Square pyramid Wikipedia