
 Great Rhombicuboctahedron 
 Vertex description: 4.3/2.4.4
 Faces: 26
 Edges: 48
 Vertices: 24
 External facelets: 488
 Dual: Great strombic icositetrahedron
 Name breakdown:
 Great: To distinguish polyhedra that would otherwise have the
same name.
 Rhombi: 12 faces (squares) lie parallel to those of a
rhombic dodecahedron
 cub: 6 more faces (squares) lie parallel to those of a
cube
 octa: 8 faces (triangles) lie parallel to those of an
octahedron
A uniform polyhedron whose faces consist of 18 squares (12 red, 6 blue) and
8 triangles (yellow). It is a faceting of the
truncated cube, that is, it shares the
same vertices. It also shares the same vertices with the
great Cubicuboctahedron and the
great rhombihexahedron. In fact all
but the truncated cube share the same edges too.
Three squares and one triangle meet at each vertex.
The squares come in two colours, as they fit into the model in two distinct
ways. The six blue squares are in planes parallel to the faces of a cube, while the twelve red squares lie in planes parallel
to the faces of a rhombic dodecahedron.
The description above also applies to the
rhombicuboctahedron (with different
colours). The two models are isomorphic since they share the same
topology.

There's a bit of work required to build this model. It has 488
external facelets, and 876 external edgelets.
Great Stella
helps by joining facelets into nets, and each join saves you having to
score, fold and glue an edge.
Shown here is one of the octagram parts completed.


Here is the same octagram part upsidedown. Basically you make six of
these and then put all the remaining pieces together as you would the
great cubicuboctahedron.


Here the model starts to take shape, with two octagram parts and a few
connecting pieces in place.


Various parts inside can be glued together to add strength. The tips
of the deepest recesses of the octagram parts touch each other between
neighbouring parts, and so the tabs at their ends may be glued
together (you might want to click on the image for a closer look).
The octagram parts themselves are also quite floppy, so I have glued
rectangles to the alreadyglued double tabs along the sides of the
inner square of yellow edges. This keeps things in place quite well.


Also, there are parts of the model which touch each other only along an
edge. I have used
Great Stella's
"Internal Support" option from the
"Nets>Coincident Edge Method" submenu (which is the
default) when generating these nets, which results in there being a
glued double tab on one side of these edges, and no tab (just a fold in
the net) on the other side. If you look at the upsidedown octagram
part above, you can see that the outer radiating ridges alternate
between tab and no tab. These double tabs are then glued to the back
of the face from the touching net.


Now for putting those last pieces in! The final octagram part should
be completed on its own before putting it in place. The good thing is
that you can still fold it up along those yellow edges, due to the way
I strengthened them. I suggest putting all the blue corner pieces in,
but leaving off the yellow doubletriangle parts till the end. Here
the final octagram part has been glued to one of the blue corner
pieces, and is folded up along one of those yellow edges.


Now the lid is closed, and each of the final three sections can be
folded down and glued in place.


Before gluing those final sections down though, I reached in with
tweezers to glue those neighbouring deep octagram recesses together
(you can just see it in the dark in there!). Finally the last
four yellow doubletriangle parts can be glued in place.


This model fitted together surprisingly well in the end, and you'd
never be able to tell which bit went in last (even I can't!). Here we
see the completed model, standing on one of its 3fold symmetry
axes. Looking at the model, you wouldn't really think of it being able
to stand this way, but it does!


The view down a 4fold rotational symmetry axes.


The view down a 3fold rotational symmetry axes.


The view down a 2fold rotational symmetry axes.


This shows how big the model is. It has an edge length (or height,
when sitting on its 4fold axis) of about 14.5 cms.

