Editing Disdyakis dodecahedron (section)

{{Short description|Catalan solid with 48 faces}}
{| class=wikitable align=right width="250"
!bgcolor=#e7dcc3 colspan=2|Disdyakis dodecahedron
|-
|align=center colspan=2|[[Image:disdyakisdodecahedron.jpg|240px|Disdyakis dodecahedron]]<br>([[:image:disdyakisdodecahedron.gif|rotating]] and [[:File:Disdyakis dodecahedron.stl|3D]] model)
|-
|bgcolor=#e7dcc3|Type||[[Catalan solid]]
|-
|bgcolor=#e7dcc3|[[Conway polyhedron notation|Conway notation]]||mC
|-
|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_f1|4|node_f1|3|node_f1}}
|-
|bgcolor=#e7dcc3|Face polygon||[[File:DU11 facets.png|60px]]<br>[[scalene triangle]]
|-
|bgcolor=#e7dcc3|Faces||48
|-
|bgcolor=#e7dcc3|Edges||72
|-
|bgcolor=#e7dcc3|Vertices||26 = 6 + 8 + 12
|-
|bgcolor=#e7dcc3|[[Face configuration]]||V4.6.8
|-
|bgcolor=#e7dcc3|[[List of spherical symmetry groups|Symmetry group]]||''O''<sub>''h''</sub>, B<sub>3</sub>, [4,3], *432
|-
|bgcolor=#e7dcc3|[[Dihedral angle]]||155° 4' 56"<br><math>\arccos(-\frac{71 + 12\sqrt{2}}{97})</math>
|-
|bgcolor=#e7dcc3|[[Dual polyhedron]] || [[File:Polyhedron great rhombi 6-8 max.png|70px]]<br>[[truncated cuboctahedron]]
|-
|bgcolor=#e7dcc3|Properties||convex, [[face-transitive]]
|-
|align=center colspan=2|[[File:Disdyakis 12 net.svg|200px|Disdyakis dodecahedron]]<br>[[Net (polyhedron)|net]]
|}
In [[geometry]], a '''disdyakis dodecahedron''', (also '''hexoctahedron''',<ref>{{cite web |url=https://etc.usf.edu/clipart/keyword/forms |title = Keyword: "forms" {{!}} ClipArt ETC}}</ref> '''hexakis octahedron''', '''octakis cube''', '''octakis hexahedron''', '''kisrhombic dodecahedron'''<ref>Conway, Symmetries of things, p.284</ref>) or '''d48''', is a [[Catalan solid]] with 48 faces and the dual to the [[Archimedean solid|Archimedean]] [[truncated cuboctahedron]]. As such it is [[face-transitive]] but with irregular face polygons. It resembles an augmented [[rhombic dodecahedron]]. Replacing each face of the rhombic dodecahedron with a flat pyramid results in the [[Kleetope]] of the rhombic dodecahedron, which looks almost like the disdyakis dodecahedron, and is [[topology|topologically]] equivalent to it.{{Efn|Despite their resemblance, no subset of the disdyakis dodecahedron's vertices forms a rhombic dodecahedron (see [[#Cartesian coordinates]]), and therefore, the former is not the Kleetope of the latter. The "rhombic" bases of the pyramids of the disdyakis dodecahedron are in fact not even planar; for example, the vertices of one such rhombus are (a, 0, 0), (0, a, 0), (c, c, c), (c, c, -c) (again, see [[#Cartesian coordinates]] for the values of a and c), with diagonal midpoints (√2)×(a, a, 0) and (c, c, 0), which do not coincide.}} The net of the [[rhombic dodecahedral pyramid]] also shares the same topology.