AugmentedPolyhedron

AugmentedPolyhedron[poly]

gives the augmented polyhedron poly by replacing each face by a pyramid.

AugmentedPolyhedron[poly,h]

gives the augmented polyhedron with a pyramid of height h.

Details and Options

Examples

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Basic Examples  (2)

Augmented polyhedron of a dodecahedron:

Find the augmented polyhedron of the space shuttle:

Visualization:

Scope  (4)

AugmentedPolyhedron works on polyhedra:

AugmentedPolyhedron of Platonic solids includes Tetrahedron:

Cube:

Dodecahedron:

Octahedron:

Icosahedron:

Support polyhedron meshes:

Augment the polyhedron by different heights:

Applications  (4)

Basic Applications  (3)

Gallery of Platonic solids and their augmented polyhedra:

Gallery of Archimedean solids and their augmented polyhedra:

Augmented compounds of Platonic solids:

Archimedean solids:

Polyhedron Operations  (1)

Use AugmentedPolyhedron to compute the polyhedron operations such as zip operation:

Properties & Relations  (1)

The augmented simple polyhedron is simple:

Possible Issues  (2)

AugmentedPolyhedron only supports simple polyhedra:

AugmentedPolyhedron can return degenerate polyhedra:

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

Text

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

CMS

Wolfram Language. 2019. "AugmentedPolyhedron." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html.

APA

Wolfram Language. (2019). AugmentedPolyhedron. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html

BibTeX

@misc{reference.wolfram_2025_augmentedpolyhedron, author="Wolfram Research", title="{AugmentedPolyhedron}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html}", note=[Accessed: 09-May-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_augmentedpolyhedron, organization={Wolfram Research}, title={AugmentedPolyhedron}, year={2019}, url={https://reference.wolfram.com/language/ref/AugmentedPolyhedron.html}, note=[Accessed: 09-May-2025 ]}