Merge two cubes. (Cuboctahedron)

Questions
,
1

I need to create a Cuboctahedron.

Cuboctahedron_by_Cutting_Rhombic_Dodecahedron.svg.png
Cuboctahedron_by_Cutting_Rhombic_Dodecahedron.svg.png1000×1000 86.9 KB

I was able to build a cube or cylinder by using Cylinder or Cube Methods…
I found the Polyhydron[“Cuboctahedron”] method and wondered
What is different between:

c = Cylinder[...]
vs
c = Polyhydron["Cuboctahedron"]

As i can’t figure out what the difference is i am trying to merge two cubes to get the same effect.
It seems to me that I can create two cubes and rotate one of the 45,45,45…
Then I can use RegionDifference to create the object…
However I’m not sure I know. how to rotate the second 3D cube 45,45,45..
Help?

2

Maybe this will help

Entity["Polyhedron", "Cuboctahedron"]["Dataset"]
3

The following code shows a ball being combined with a cylinder.
I need to change the ball to the Cuboctahedron.
This section of code works:

cy = Cylinder[{{-1, 0, 0}, {1, 0, 0}}, .25];
ba = Ball[{0, 0, 0}, 1];
sc = PolyhedronData["Cuboctahedron"];
rd = RegionDifference[ba, cy];
o = RegionPlot3D[rd, PlotPoints -> 42]

However this code fails:

rd = RegionDifference[sc, cy];
o = RegionPlot3D[rd, PlotPoints -> 42]

And I don’t know why.

4

PolyhedronData[“Cuboctahedron”] returns a Graphics3D object, so cannot be used with RegionDifference. But PolyhedronData[“Cuboctahedron”,“ImplicitRegion”] will return a region.

cy = Cylinder[{{-1, 0, 0}, {1, 0, 0}}, .25];
sc = PolyhedronData["Cuboctahedron", "ImplicitRegion"];
rd = RegionDifference[sc, cy];
RegionPlot3D[rd, PlotPoints -> 42, Boxed -> False]

Cuboctahedron.png
Cuboctahedron.png305×301 17 KB

5

Thank you!
Unlike the Cylinder method which you can supply additional parameters, the Polyhydron method seems to lack constructors, how does one apply a scale and rotation to this object at construction?

I was afraid to say that the return type seems typeless… but it does. I am relieved to here it does have a type… but why am i not seeing that in the documentation the method? Am i missing something?

6

An example of applying rotation:

cuboctas = Table[
   	Rotate[PolyhedronData["Cuboctahedron", "Polyhedron"], i Degree, {0, 0, 1}],
   	{i, 0, 90, 15}
  ];

Manipulate[
 	Graphics3D[cuboctas[[angle]], Axes -> True, PlotRange -> 1.1],
 	{{angle, 1}, {1 -> 0, 2 -> 15, 3 -> 30, 4 -> 45, 5 -> 60, 6 -> 75, 7 -> 90}, SetterBar},
 	SaveDefinitions -> True
 ]

See also the functions Scale and Translate