n433 polyhedra
8433 (left) and
10433
(right)
The solutions to the 8433
and 10433 acrons are obviously
related.
They are members of a family of polyhedra formed by wrapping a complex
of squares and triangles between two polygons. The squares
are in strips of three, the triangles are in complexes of fourteen.
In addition to the
above
linked octagonal and decagonal models, examples can be formed for other
ngons, where n is even. The figures continue
above
n=12,but
as
there
is
now
an
angular
excess
the
triangular
complexes
become
folded.
n433 with n odd
'7'433
Due to the alternating nature
of the connecting squares and triangles, examples cannot be formed
where
n is odd. However a closely related toroidal family can be
generated
by utilising the degenerate 2n/2gons (such as the 14/2gon).
Examples
generated using these polygons can then have the base polygons removed
leaving the edges of the square and triangular rings
connected.
The resulting toroid has an ngonal prismatic symmetry. A number
of examples are included in the zip files below.
Again, models can be generated for n/d where d>1:
Again a number of examples are included in the zip files below.
Isomerism
There are
a number of distinct isomers for each n  although some appear to have
limits as shown below. The names are
informal and are intended solely as an aid to recognition. It is not known if
the list below is complete.
The
zip files linked below each model contain WRL, OFF and TXT files for
each
model in the range. Where they can be generated, models are
included for n = 5/2, 3,
7/2,
4,
9/2,
5,
11/2,
6,
7,
8,
9,
10,
11,
12,
14,
16.
The links
in the above list are zip files of each isomer for that value of
n. A large zip file containing both sets of zip files is here.
Note that
in the isomer specific zip files below the star polygons have been
renamed, for example, 5/2 is renamed 2d5 (2 decimal 5). This is
so the models are presented in strict sequence of increasing X.
6433_exo WRL
OFF 
6433_endo WRL
OFF 
6433_inverted
exo WRL OFF n433_inverted_exo.zip (n = 5/2  16) 
6433 endo crossed WRL OFF n433_endo_crossed.zip (n = 4  16) 

6433 folded WRL OFF n433_folded.zip (n = 5/2  14) 



6433 exo
folded WRL OFF n433_exo_folded.zip (n = 5/2  16) 
6433_chiral WRL
OFF n433_chiral.zip (n = 5/2  16) 
6433 inverted
exo
chiral WRL
OFF n433_inverted_exo_chiral.zip (n = 5/2  16) 
6433 chiral
folded WRL OFF n433_chiral_folded.zip (n = 5/2  12) 
n433_chiral_saucer.zip (n = 4  16) 
6433 exo chiral
folded WRL OFF n433_exo_chiral_folded.zip (n = 5/2  16) 

6433 crowned hatbox WRL OFF 
6433 lighthouse WRL OFF n433_lighthouse.zip (n = 4  16) 
6433 crown WRL
OFF n433_crown.zip (n = 9/2  16) 4 is degenerate 
6433 crown2
WRL OFF n433_crown2.zip (n = 9/2  12) 

6433 hatbox WRL
OFF n433_hatbox.zip (n = 5/2  16) 


The everted form is
remarkably
similar to 'cup' but they are two distinct forms. 

n3333 acrohedra.
43333
WRL 
OFF 

exo 
3 4 5 6 7  3 4 5 6 7 
endo 
8 9 10 11 12 14
15 16 17 18 
8 9 10 11 12 14 15 16 17 18 