Square pyramid (EntityTopic, 23)

From Hi.gher. Space

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{{STS Shape
{{STS Shape
| dim=3
| dim=3
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| elements=5, 8, 5
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| elements=1 [[square]], 4 [[triangle]]s, 8 [[digon]]s, 5 [[point]]s
| sym=[[Stauroaxial symmetry|C<sub>4v</sub>]]
| sym=[[Stauroaxial symmetry|C<sub>4v</sub>]]
| genus=0
| genus=0
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A '''square pyramid''' is a special case of a [[pyramid]] where the base is a [[square]].
A '''square pyramid''' is a special case of a [[pyramid]] where the base is a [[square]].
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The square pyramid with equilateral triangular sides is the first of the 92 Johnson solids, and is referred to as J<sub>1</sub>. It can be obtained from an [[octahedron]] by cutting it in half.
== Equations ==
== Equations ==

Revision as of 02:08, 26 March 2017

A square pyramid is a special case of a pyramid where the base is a square.

The square pyramid with equilateral triangular sides is the first of the 92 Johnson solids, and is referred to as J1. It can be obtained from an octahedron by cutting it in half.

Equations

  • Variables:
l ⇒ length of edges of the square pyramid
total edge length = 8l
surface area = (1 + √3) · l2
volume = √26 · l3
[!x,!y] ⇒ triangle
[!z] ⇒ square

Incidence matrix

Dual: Self-dual

#TXIDVaVbEaEb3a4aTypeName
0 Va = point ; sweep: apex
1 Vb = point ; lateral: vertices
2 Ea 11 = digon ; sweep: vertices
3 Eb 02 = digon ; lateral: edges
4 3a 1221 = triangle ; sweep: edges
5 4a 0404 = base of pyramid: square ; lateral: faces
6 C1a 144441 = square pyramid ;

Usage as facets


Notable Trishapes
Regular: tetrahedroncubeoctahedrondodecahedronicosahedron
Direct truncates: tetrahedral truncatecubic truncateoctahedral truncatedodecahedral truncateicosahedral truncate
Mesotruncates: stauromesohedronstauroperihedronstauropantohedronrhodomesohedronrhodoperihedronrhodopantohedron
Snubs: snub staurohedronsnub rhodohedron
Curved: spheretoruscylinderconefrustumcrind


8. 21
Cone
9. [11]1
Square pyramid
10. 111
Triangular prism
List of tapertopes