Square pyramid (EntityTopic, 23)

From Hi.gher. Space

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{{Shape|Square pyramid|''No image''|3|5, 8, 5|0|N/A|N/A|[[Line (object)|E]][[Square|E]]T|11<sup>1</sup> xy<sup>z</sup>|N/A|N/A|N/A|6|N/A|N/A|pure}}
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<[#ontology [kind topic] [cats Square Pyramid 3D Polytope] [alt [[freebase:048qg3]] [[wikipedia:Square_pyramid]]]]>
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== Geometry ==
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{{STS Shape
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| dim=3
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| elements=5, 8, 5
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| sym=[[Stauroaxial symmetry|C<sub>4v</sub>]]
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| genus=0
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| ssc=G4P
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| ssc2=&G4
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| extra={{STS Matrix|
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<i>2 2</i>
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4 0
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1 1}}{{STS Tapertope
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| order=2, 1
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| notation=[11]<sup>1</sup>
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| index=9
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}}{{STS Polytope
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| flayout={{FLD|a4|i|ade|cr|e4}}
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| dual=''Self-dual''
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| bowers=Squippy
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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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=== Equations ===
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== Equations ==
*Variables:
*Variables:
<blockquote>''l'' ⇒ length of edges of the square pyramid</blockquote>
<blockquote>''l'' ⇒ length of edges of the square pyramid</blockquote>
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*The [[hypervolume]]s of a square pyramid are given by:
*The [[hypervolume]]s of a square pyramid are given by:
<blockquote>total edge length = 8''l''<br>
<blockquote>total edge length = 8''l''<br>
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surface area = ''l''<sup>2</sup>(1+2√3)<br>
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surface area = (1 + √3) {{DotHV}}<br>
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volume = ''l''<sup>3</sup>6<sup>-1</sup>√2</blockquote>
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volume = {{Over|√2|6}} {{DotHV|3}}</blockquote>
*The [[planar]] [[cross-section]]s (''n'') of a square pyramid are:
*The [[planar]] [[cross-section]]s (''n'') of a square pyramid are:
<blockquote>[!x,!y] ⇒ [[triangle]]<br>
<blockquote>[!x,!y] ⇒ [[triangle]]<br>
[!z] ⇒ square</blockquote>
[!z] ⇒ square</blockquote>
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<[#polytope [id 44]]>
{{Trishapes}}
{{Trishapes}}
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{{Rotope Nav|5|6|7|III<br>Cube|II'<br>Square pyramid|(III)<br>Sphere|hedra}}
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{{Tapertope Nav|8|9|10|2<sup>1</sup><br>Cone|[11]<sup>1</sup><br>Square pyramid|11<sup>1</sup><br>Triangular prism|hedra}}

Revision as of 22:08, 2 March 2014

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

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