Editing Truncated cuboctahedron (section)

== Dissection ==
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The truncated cuboctahedron is the [[convex hull]] of a [[rhombicuboctahedron]] with cubes above its 12 squares on 2-fold symmetry axes. The rest of its space can be dissected into 6 [[square cupola]]s below the octagons, and 8 [[triangular cupola]]s below the hexagons.

A dissected truncated cuboctahedron can create a genus 5, 7, or 11 [[Stewart toroid]] by removing the central rhombicuboctahedron, and either the 6 square cupolas, the 8 triangular cupolas, or the 12 cubes respectively. Many other lower symmetry toroids can also be constructed by removing the central rhombicuboctahedron, and a subset of the other dissection components. For example, removing 4 of the triangular cupolas creates a genus 3 toroid; if these cupolas are appropriately chosen, then this toroid has tetrahedral symmetry.<ref>B. M. Stewart, ''[[Adventures Among the Toroids]]'' (1970) {{isbn|978-0-686-11936-4}}</ref><ref>{{cite web|url=http://www.doskey.com/polyhedra/Stewart05.html|title=Adventures Among the Toroids - Chapter 5 - Simplest (R)(A)(Q)(T) Toroids of genus p=1|first=Alex|last=Doskey|website=www.doskey.com}}</ref>

{| class="wikitable collapsible collapsed"
!colspan="4"| Stewart toroids
|-
!Genus 3
!Genus 5
!Genus 7
!Genus 11
|-
|[[File:Excavated truncated cuboctahedron4.png|160px]]
|[[File:Excavated truncated cuboctahedron2.png|160px]]
|[[File:Excavated truncated cuboctahedron3.png|160px]]
|[[File:Excavated truncated cuboctahedron.png|160px]]
|}