Editing Disdyakis dodecahedron (section)

==Cartesian coordinates==                                                                                                                                    
Let <math> ~ a = \frac{1}{1 + 2 \sqrt{2}} ~ {\color{Gray} \approx 0.261}, ~~ b = \frac{1}{2 + 3 \sqrt{2}} ~ {\color{Gray} \approx 0.160}, ~~ c = \frac{1}{3 + 3 \sqrt{2}} ~ {\color{Gray} \approx 0.138}</math>.<br> 
Then the [[Cartesian coordinates]] for the vertices of a disdyakis dodecahedron centered at the origin are:

{{color|#eb2424|●}} &nbsp; [[permutation]]s of (±'''a''', 0, 0) &nbsp; <small>(vertices of an octahedron)</small><br>
{{color|#3061d6|●}} &nbsp; permutations of (±'''b''', ±'''b''', 0) &nbsp; <small>(vertices of a [[cuboctahedron]])</small><br>
{{color|#f9b900|●}} &nbsp; (±'''c''', ±'''c''', ±'''c''') &nbsp; <small>(vertices of a cube)</small>

{| class="wikitable collapsible collapsed" style="text-align: left;"
!colspan="1" width=400|[[Convex hull|Convex hulls]]
|-
|Combining an octahedron, cube, and cuboctahedron to form the disdyakis dodecahedron. The convex hulls for these vertices<ref>{{cite journal
|title=Catalan Solids Derived From 3D-Root Systems and Quaternions
|first1=Mehmet
|last1=Koca
|first2=Nazife
|last2=Ozdes Koca
|first3=Ramazon
|last3=Koc
|year=2010
|journal=Journal of Mathematical Physics
|volume=51
|issue=4
|doi=10.1063/1.3356985 
|arxiv=0908.3272
}}</ref> scaled by <math>1/a</math> result in Cartesian coordinates of unit [[circumradius]], which are visualized in the figure below:
|-
|rowspan="1"|[[File:Disdyakis Dodecahedron convex hulls.svg|400px|Combining an octahedron, cube, and cuboctahedron to form the disdyakis dodecahedron]]

|-
|}