
 Pseudo Great Rhombicuboctahedron 
 Vertex description: 4.3/2.4.4 (but nonuniform overall)
 Faces: 26
 Edges: 48
 Vertices: 24
 External facelets: 424
 Dual:
Pseudo great strombic icositetrahedron
 Name breakdown:
 Pseudo: A nonuniform variation, only possible with two uniform
polyhedra.
 Great Rhombicuboctahedron: The uniform polyhedron being varied.
See great rhombicuboctahedron.
This is the pseudo version of the
great rhombicuboctahedron. See the
pseudo rhombicuboctahedron for a simpler
example of a pseudouniform polyhedron (they are actually topologically
identical to these more complex models!). Here again, the pseudo model may be
thought of as having one section twisted with respect to the true
uniform model, but it is much harder to visualise, and the vertices are still
all surrounded by faces in the same way (three squares and one retrograde
triangle). The symmetry group of the pseudo model is 4fold dihedral, same as
that of the square antiprism.
This model is the dual of the
pseudo great strombic icositetrahedron.
To get this model in
Great Stella,
start by selecting the "Great Rhombicuboctahedron" from the list, then select
the "Poly>Create Pseudo Version" menu item.

Here you see one of each different type of net required to build
the model. There are a lot!


And here are all the nets. A box with compartments helps a lot
to keep the pieces organised. As you can see, there aren't enough
compartments for all the different kinds of pieces, but I group pieces
together that will be directly connected. The
great rhombicuboctahedron may have
slightly more external facelets (488 versus 424), but this model is a
bit trickier to construct. The smallest pieces are smaller, and
there's certainly more variety along the way.


As with the nonpseudo version, we start by building one of these
octagram parts. Note the different colour arrangement however, and you
only need two of these parts, rather than six.


Next put together four of this part.


You'll also need four of these parts (shown here in stages of
completion).


The above eight parts can then be glued around one of the octagram
parts, as shown. The model so far has a big green square as its base.


Here is the same thing upsidedown. The big green square stands out.
The next set of parts will be glued around each edge of this green
square.


The two nets shown here fold up to create pieces that are mirror images
of each other, but note that the cut required to flatten the net is
along a different edge. By default,
Great Stella
creates both nets like the one on the right, but cutting the shorter
edge like the one on the left leads to nets that pack better onto the
page when printing, and the edges requiring gluing are shorter. So I
used
"Selection>Mouse Selection Mode>Cut/Uncut Edges"
mode, and then Shift+LeftClick on the shorter edge of one of
these pieces, to cut that edge instead of the longer one. Only do this
to one of the two nets though, since the longer tabs from the other net
will be useful for gluing behind other faces later.


Put together these pieces as shown.


And these in turn go together to make this part. You will see now how
that long tab is used to glue the deep sections together behind the big
yellow face. You need to make four of these.


Glue those four parts to the four edges of the big green square from
earlier. I have also glued an extra piece of paper along each edge for
added strength.


These four parts then fold up and glue in place using more of those
long tabs.


Now fill in the gaps around this level, leaving a big square around the
opening.


Then add everything except for the second octagram part and its four
surrounding yellow triangle pairs, to get what's shown here. Most of
this can be constructed separately, and then glued on in just a few
parts. Finally, glue the octagram part in place, same as the last
octagram part of the
great rhombicuboctahedron was, and add
the final four yellow triangle pairs to complete the model.


The view down a 4fold rotational symmetry axes.


The view down a 2fold rotational symmetry axes.

