In 1995, R. Hughes Jones [__Enumerating uniform polyhedral surfaces
with triangular faces__, R. Hughes Jones, *Discrete Mathematics*,
Vol. 138 (1995), pp. 281-292.] noted that vertex stars made up entirely
of regular triangles could be created using a cuboctahedron as a template.
Consider a cuboctahedron centered at the origin where the distance from
the origin to any vertex of the cuboctahedron is the same as the
cuboctahedron's edge length. Then any two adjacent vertices of the
cuboctahedron along with the center form a regular triangle. A
Hamiltonian cycle is a path along the edges that visits a subset of the
vertices, but each vertex only once (except for the final point), and
that ends with the same vertex as its start. By then forming the
triangles created using the edges of the path, each edge joined with the
cuboctahedron center to make a regular triangle, a vertex star can be
created. For example, one of the faces of the cuboctahedron is a
triangle. Traveling around this triangle forms a Hamiltonian cycle with
three vertices. Each of these three edges can be joined with the center
to make three triangles attached adjacently around a central vertex (the
origin), and which combined together form a vertex star. In fact, this
vertex star is the one used to construct a tetrahedron. Many other
cyclic paths exist on the cuboctahedron. As another example, a path
around the diameter forms a planar hexagon and this vertex star creates
the {3,6} planar tiling vertex star. In fact, Hughes Jones found 52
such paths, each forming a vertex star. Of these 52 vertex stars, 22 of
them form polyhedra. There are 32 of them, though 2 are essentially the
same; of these remaining 31, 2 are finite and 3 are infinite in two
dimensions only and are described elsewhere here on other pages. That
leaves 26 three-dimensionally infinite sponges. Of these 26, there is 1
with 7 triangles in its vertex star, 3 with 8, 13 with 9, and 9 with 12.
(While the cuboctahedron generates vertex stars having 10 or 11
triangles, none of them form sponges.) Without a doubt, the sponges
having 12 triangles in their vertex stars are very difficult to
visualize!

The smallest vertex star created in this way is the one described above
that forms the tetrahedron.
The next largest one has four triangles and forms the
octahedron. These are the two
finite polyhedra. No polyhedron can be created from the five-triangle
vertex star. Then there are four {3,6} vertex stars, each creating
two-dimensional infinite polyhedra: the first is the coplanar one
that creates the {3,6} planar tiling
(as mentioned above), the second is the
crinkled {3,6} polyhedron, and
the final two form folded {3,6}
polyhedra. These last two differ only in the dihedral angle of their
fold and since they form essentially the same polyhedra they can
be considered to be identical for the purposes considered here.
Together these form the 6 polyhedra separated from the possible 32
above, leaving 26 remaining infinite sponges formed using 16
different vertex stars. The sponges and their vertex stars are listed
and named below using the order and notation Hughes Jones assigned them.
In these cases, 3^{n} corresponds to {3,n}, with
P_{i} referring to polyhedra and V_{i}
referring to vertex stars. Hughes Jones also used an adjacency labeling
related to the dihedral angles rather than the edges of the vertex star.
We do not report these below, but instead only our own assigned
incidence symbols. Because of the large number of polygons some of them
contain and the unusual symmetries they are thus able to possess, many
of them use some of the most exotic vertex and adjacency symbol
notations we have encountered so far.

Hughes Jones only reported the different geometric shapes but not the number of different labelings that the symmetric sponges could support. Therefore these have been added here. When only a single labeling appears it is because there are no symmetries that can support multiple labelings. Finally, for the first six polyhedra their multiple labelings are reported on the other pages where these polyhedra have already appeared.

- (3
^{3})V_{1}tetrahedron - (3
^{4})V_{1}octahedron - (3
^{6})V_{1}folded {3,6} - (3
^{6})V_{2}crinkled {3,6} - (3
^{6})V_{3}folded {3,6} - (3
^{6})V_{4}{3,6} planar tiling - (3
^{7})P_{1}(3^{7})V_{3}- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}; a^{+}f^^{+}d^{+}c^{+}g^^{+}b^^{+}e^^{+}]

- [a
- (3
^{8})P_{1}(3^{8})V_{5}- [a
^{+}b^{+}c^{+}d^{+}d^{-}c^{-}b^{-}a^{-}; b^{+}a^{+}c^{-}d^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}; b^{+}a^{+}f^{+}d^{+}e^{+}c^{+}h^{+}g^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}; b^{+}a^{+}f^{+}e^{-}d^{-}c^{+}h^{+}g^{+}]

- [a
- (3
^{8})P_{2}(3^{8})V_{6}- [a
^{+}b^{+}c^{+}d^{+}a^{+}b^{+}c^{+}d^{+}; a^{+}c^{+}b^{+}d^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}; a^{+}c^{+}b^{+}h^{+}e^{+}g^{+}f^{+}d^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}; e^{+}c^{+}b^{+}d^{+}a^{+}g^{+}f^{+}h^{+}]

- [a
- (3
^{8})P_{3}(3^{8})V_{3}- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}; a^{+}c^{+}b^{+}h^{+}f^{+}e^{+}g^{+}d^{+}]

- [a
- (3
^{9})P_{1}(3^{9})V_{6}- [a b
^{+}b^{-}a b^{+}b^{-}a b^{+}b^{-}; a b^{+}b^{-}] - [a
^{+}b^{+}c^{+}a^{+}b^{+}c^{+}a^{+}b^{+}c^{+}; a^{+}b^{+}c^{+}] - [a
^{+}b^{+}c^{+}a^{+}b^{+}c^{+}a^{+}b^{+}c^{+}; a^{+}c^{-}b^{-}] - [a b
^{+}c^{+}d^{+}e^{+}e^{-}d^{-}c^{-}b^{-}; a e^{+}c^{+}d^{+}b^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^{+}c^{+}d^{+}b^{+}i^{+}g^{+}h^{+}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^{+}h^{-}g^{-}b^{+}i^{+}d^{-}c^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}f^{-}c^{+}g^{-}i^{-}b^{-}d^{-}h^{+}e^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}f^{-}h^{-}d^{+}i^{-}b^{-}g^{+}c^{-}e^{-}]

- [a b
- (3
^{9})P_{2}(3^{9})V_{4}- [a b
^{+}c^{+}d^{+}e^{+}e^{-}d^{-}c^{-}b^{-}; a e^^{-}c^{+}d^^{-}b^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^^{-}c^{+}d^^{-}b^^{-}i^^{-}g^^{-}h^{+}f^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^^{-}h^{-}g^^{+}b^^{-}i^^{-}d^^{+}c^{-}f^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}f^^{+}c^{+}g^^{+}i^^{+}b^^{+}d^^{+}h^{+}e^^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}f^^{+}h^{-}d^^{-}i^^{+}b^^{+}g^^{-}c^{-}e^^{+}]

- [a b
- (3
^{9})P_{3}(3^{9})V_{8}- [a b
^{+}c^{+}d^{+}e^{+}e^{-}d^{-}c^{-}b^{-}; a e^{+}c^{+}d^{+}b^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^{+}c^{+}d^{+}b^{+}i^{+}g^{+}h^{+}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^{+}h^{-}g^{-}b^{+}i^{+}d^{-}c^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}f^{-}c^{+}g^{-}i^{-}b^{-}d^{-}h^{+}e^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}f^{-}h^{-}d^{+}i^{-}b^{-}g^{+}c^{-}e^{-}]

- [a b
- (3
^{9})P_{4}(3^{9})V_{8}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; c^^{+}f^^{-}a^^{+}g^{-}i^{-}b^^{-}d^{-}h^{+}e^{-}]

- [a
- (3
^{9})P_{5}(3^{9})V_{2}- [a b
^{+}c^{+}d^{+}e^{+}e^{-}d^{-}c^{-}b^{-}; a e^^{-}c^^{-}d^{+}b^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^^{-}c^^{-}d^{+}b^^{-}i^^{-}g^{+}h^^{-}f^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^^{-}h^^{+}g^{-}b^^{-}i^^{-}d^{-}c^^{+}f^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}f^^{+}c^^{-}g^{-}i^^{+}b^^{+}d^{-}h^^{-}e^^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}f^^{+}h^^{+}d^{+}i^^{+}b^^{+}g^{+}c^^{+}e^^{+}]

- [a b
- (3
^{9})P_{6}(3^{9})V_{3}- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^^{-}c^{+}d^^{-}b^^{-}i^^{-}g^{+}h^^{-}f^^{-}]

- [a
- (3
^{9})P_{7}(3^{9})V_{3}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^^{-}g^{+}h^^{-}b^^{-}i^^{-}c^{+}d^^{-}f^^{-}]

- [a
- (3
^{9})P_{8}(3^{9})V_{7}- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^{+}c^{+}d^{+}b^{+}i^{+}g^{+}h^{+}f^{+}]

- [a
- (3
^{9})P_{9}(3^{9})V_{7}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}e^{+}g^^{-}h^^{-}b^{+}i^{+}c^^{-}d^^{-}f^{+}]

- [a
- (3
^{9})P_{10}(3^{9})V_{9}- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}g^^{+}c^^{-}h^{-}e^^{-}i^^{+}b^^{+}d^{-}f^^{+}]

- [a
- (3
^{9})P_{11}(3^{9})V_{9}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}g^^{+}e^^{+}h^{+}c^^{+}i^^{+}b^^{+}d^{+}f^^{+}]

- [a
- (3
^{9})P_{12}(3^{9})V_{1}- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}g^^{+}c^{+}h^^{+}e^{+}i^^{+}b^^{+}d^^{+}f^^{+}]

- [a
- (3
^{9})P_{13}(3^{9})V_{1}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}; a^{+}g^^{+}e^{-}h^^{-}c^{-}i^^{+}b^^{+}d^^{-}f^^{+}]

- [a
- (3
^{12})P_{1}(3^{12})V_{5}- [a*
^{+}b^{+}c^{+}d*^{+}c^^{+}b^^{+}a*^{+}b^{+}c^{+}d*^{+}c^^{+}b^^{+}; d*^{-}b^{+}c^^{-}a*^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}a^{+}b^{+}c^{+}d^{+}e^{+}f^{+}; d^^{-}b^{+}c^^{-}a^^{-}e^^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}a^{+}b^{+}c^{+}d^{+}e^{+}f^{+}; d^{-}b^{+}e^{-}a^{-}c^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}a^{+}b^{+}c^{+}d^{+}e^{+}f^{+}; d^{-}f^^{+}c^^{-}a^{-}e^^{-}b^^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}a^{+}b^{+}c^{+}d^{+}e^{+}f^{+}; d^^{-}f^^{+}e^{-}a^^{-}c^{-}b^^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; d^^{-}b^{+}c^^{-}a^^{-}e^^{-}l^{+}j^^{-}h^{+}i^^{-}g^^{-}k^^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; d^^{-}b^{+}c^^{-}a^^{-}k^^{-}f^{+}j^^{-}h^{+}i^^{-}g^^{-}e^^{-}l^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; d^^{-}h^{+}i^^{-}a^^{-}e^^{-}l^{+}j^^{-}b^{+}c^^{-}g^^{-}k^^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; d^^{-}h^{+}i^^{-}a^^{-}k^^{-}f^{+}j^^{-}b^{+}c^^{-}g^^{-}e^^{-}l^{+}]

- [a*
- (3
^{12})P_{2}(3^{12})V_{4}- [a
^{+}b^{+}c^{+}a^^{-}b^^{-}c^^{-}a^{+}b^{+}c^{+}a^^{-}b^^{-}c^^{-}; a^{+}b^^{-}c^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}a^{+}b^{+}c^{+}d^{+}e^{+}f^{+}; a^{+}b^^{-}f^^{-}d^{+}e^^{-}c^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}a^{+}b^{+}c^{+}d^{+}e^{+}f^{+}; a^{+}e^{+}c^{+}d^{+}b+^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}a^{+}b^{+}c^{+}d^{+}e^{+}f^{+}; d^^{-}b^^{-}c^{+}a^^{-}e^^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}a^{+}b^{+}c^{+}d^{+}e^{+}f^{+}; d^^{-}e^{+}f^^{-}a^^{-}b^{+}c^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; a^{+}b^^{-}l^^{-}j^{+}e^^{-}i^^{-}g^{+}h^^{-}f^^{-}d^{+}k^^{-}c^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; a^{+}e^{+}i^{+}j^{+}b^{+}l^{+}g^{+}k^{+}c^{+}d^{+}h^{+}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; a^{+}h^^{-}f^^{-}j^{+}k^^{-}c^^{-}g^{+}b^^{-}l^^{-}d^{+}e^^{-}i^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; a^{+}k^{+}c^{+}j^{+}h^{+}f^{+}g^{+}e^{+}i^{+}d^{+}b^{+}l^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; d^^{-}b^^{-}c^{+}a^^{-}e^^{-}l^{+}j^^{-}h^^{-}i^{+}g^^{-}k^^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; d^^{-}b^^{-}c^{+}a^^{-}k^^{-}f^{+}j^^{-}h^^{-}i^{+}g^^{-}e^^{-}l^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; d^^{-}h^^{-}i^{+}a^^{-}e^^{-}l^{+}j^^{-}b^^{-}c^{+}g^^{-}k^^{-}f^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; d^^{-}h^^{-}i^{+}a^^{-}k^^{-}f^{+}j^^{-}b^^{-}c^{+}g^^{-}e^^{-}l^{+}]

- [a
- (3
^{12})P_{3}(3^{12})V_{2}- [a*
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g*^{+}f^^{+}e^^{+}d^^{+}c^^{+}b^^{+}; g*^{+}e^{+}c^{+}d^{+}b^{+}f^{+}a*^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^{+}e^{+}c^{+}d^{+}b^{+}f^{+}a^{+}h^{+}l^{+}j^{+}k^{+}i^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^^{+}e^{+}k^^{+}j^^{+}b^{+}h^^{+}a^^{+}f^^{+}l^{+}d^^{+}c^^{+}i^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^{+}i^^{+}c^{+}j^^{+}l^^{+}h^^{+}a^{+}f^^{+}b^^{+}d^^{+}k^{+}e^^{+}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^^{+}i^^{+}k^^{+}d^{+}l^^{+}f^{+}a^^{+}h^{+}b^^{+}j^{+}c^^{+}e^^{+}]

- [a*
- (3
^{12})P_{4}(3^{12})V_{2}(same as previous)- [a*
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g*^{+}f^^{+}e^^{+}d^^{+}c^^{+}b^^{+}; g*^{+}e^{-}c^{+}f^{-}b^{-}d^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^{+}e^{-}c^{+}f^{-}b^{-}d^{-}a^{+}j^{-}l^{-}h^{-}k^{+}i^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^^{+}e^{-}k^^{+}h^^{-}b^{-}j^^{-}a^^{+}d^^{-}l^{-}f^^{-}c^^{+}i^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^{+}i^^{-}c^{+}h^^{-}l^^{-}j^^{-}a^{+}d^^{-}b^^{-}f^^{-}k^{+}e^^{-}] - [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^^{+}i^^{-}k^^{+}f^{-}l^^{-}d^{-}a^^{+}j^{-}b^^{-}h^{-}c^^{+}e^^{-}]

- [a*
- (3
^{12})P_{5}(3^{12})V_{2}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; g^^{+}i^^{-}k^^{+}d^{+}l^^{+}f^{+}a^^{+}j^{-}b^^{-}h^{-}c^^{+}e^^{+}]

- [a
- (3
^{12})P_{6}(3^{12})V_{3}- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; a^{+}b^^{-}l^^{-}d^{+}k^^{-}f^{+}j^^{-}h^{+}i^^{-}g^^{-}e^^{-}c^^{-}]

- [a
- (3
^{12})P_{7}(3^{12})V_{3}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; a^{+}b^^{-}l^^{-}f^{-}k^^{+}d^{-}j^^{-}h^{+}i^^{-}g^^{-}e^^{+}c^^{-}]

- [a
- (3
^{12})P_{8}(3^{12})V_{3}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; h^{+}i^^{-}l^^{-}d^{+}k^^{-}f^{+}j^^{-}a^{+}b^^{-}g^^{-}e^^{-}c^^{-}]

- [a
- (3
^{12})P_{9}(3^{12})V_{3}(same as previous)- [a
^{+}b^{+}c^{+}d^{+}e^{+}f^{+}g^{+}h^{+}i^{+}j^{+}k^{+}l^{+}; h^{+}i^^{-}l^^{-}f^{-}k^^{+}d^{-}j^^{-}a^{+}b^^{-}g^^{-}e^^{+}c^^{-}]

- [a

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