Pyramid

Pyramid[{p1,,p5}]

represents a filled pyramid with base {p1,,p4} and top p5.

Details and Options

Examples

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Basic Examples  (3)

A pyramid:

A styled pyramid:

Volume and centroid:

Scope  (18)

Graphics  (8)

Specification  (2)

A single pyramid:

Multiple pyramids:

Styling  (3)

FaceForm and EdgeForm can be used to specify the styles of the faces and edges:

Apply a Texture to the faces:

Assign VertexColors to vertices:

Coordinates  (3)

Specify coordinates by fractions of the plot range:

Specify scaled offsets from the ordinary coordinates:

Points can be Dynamic:

Regions  (10)

Embedding dimension is the dimension of the space in which the pyramid lives:

Geometric dimension is the dimension of the shape itself:

Membership testing:

Get conditions for membership:

Volume:

Centroid:

Distance from a point:

The equidistance contours for a pyramid:

Signed distance from a point:

Nearest point in the region:

Nearest points to an enclosing sphere:

A pyramid is bounded:

Find its range:

Integrate over a pyramid region:

Optimize over a pyramid region:

Solve equations in a pyramid region:

Applications  (2)

Define a regular pyramid by radius and height:

Compute its volume:

Compute its surface area:

Visualize some instances:

Find the minimum surface area for a regular pyramid with volume :

Compare with some other pyramids of the same volume:

Properties & Relations  (2)

A pyramid can be represented as the union of two tetrahedra:

Point index list of tetrahedra vertices:

ImplicitRegion can represent any Pyramid region:

Neat Examples  (1)

Sweep a pyramid around an axis:

Wolfram Research (2014), Pyramid, Wolfram Language function, https://reference.wolfram.com/language/ref/Pyramid.html (updated 2019).

Text

Wolfram Research (2014), Pyramid, Wolfram Language function, https://reference.wolfram.com/language/ref/Pyramid.html (updated 2019).

BibTeX

@misc{reference.wolfram_2021_pyramid, author="Wolfram Research", title="{Pyramid}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Pyramid.html}", note=[Accessed: 17-June-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_pyramid, organization={Wolfram Research}, title={Pyramid}, year={2019}, url={https://reference.wolfram.com/language/ref/Pyramid.html}, note=[Accessed: 17-June-2021 ]}

CMS

Wolfram Language. 2014. "Pyramid." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/Pyramid.html.

APA

Wolfram Language. (2014). Pyramid. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Pyramid.html