Square pyramid (EntityTopic, 23)

From Hi.gher. Space

(Difference between revisions)
(fix headers and equations)
m (add Bowers acronym)
(6 intermediate revisions not shown)
Line 1: Line 1:
-
<[#ontology [kind topic] [cats Square Pyramid 3D Polytope]]>
+
<[#ontology [kind topic] [cats Square Pyramid 3D Polytope] [alt [[freebase:048qg3]] [[wikipedia:Square_pyramid]]]]>
{{STS Shape
{{STS Shape
| dim=3
| dim=3
| elements=5, 8, 5
| elements=5, 8, 5
 +
| sym=[[Stauroaxial symmetry|C<sub>4v</sub>]]
| genus=0
| genus=0
| ssc=G4P
| ssc=G4P
Line 16: Line 17:
| flayout={{FLD|a4|i|ade|cr|e4}}
| flayout={{FLD|a4|i|ade|cr|e4}}
| dual=''Self-dual''
| dual=''Self-dual''
 +
| bowers=Squippy
}}}}
}}}}
-
 
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]].
Line 26: Line 27:
*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>
-
surface area = (1+2√3) {{DotHV}}<br>
+
surface area = (1 + √3) {{DotHV}}<br>
volume = {{Over|√2|6}} {{DotHV|3}}</blockquote>
volume = {{Over|√2|6}} {{DotHV|3}}</blockquote>
Line 32: Line 33:
<blockquote>[!x,!y] ⇒ [[triangle]]<br>
<blockquote>[!x,!y] ⇒ [[triangle]]<br>
[!z] ⇒ square</blockquote>
[!z] ⇒ square</blockquote>
 +
 +
<[#polytope [id 44]]>
{{Trishapes}}
{{Trishapes}}
{{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}}
{{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