Okay, we further could consider to add the Stott expansion wrt. the second node onto the former commutative diagram as well.
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qo3xx3oq4xo&#zx x . . . exp
= srico ------------> wx3xx3oq4xo&#zx
= o3x4o3x <------------
x . . . contr
^ ^
. . x . | | . . x . . . x . | | . . x .
exp | | contr exp | | contr
| | | |
v v
x . . . exp wx3xx3xw4xo&#zx
qo3xx3xw4xo&#zx ------------> = grico
<------------ = o3x4x3x
x . . . contr
Here we start with
qo3xx3oq4xo&#zx:
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qo3xx3oq4xo&#zx -> height = 0
o.3o.3o.4o. | 192 * | 2 2 2 0 | 1 2 1 1 2 2 0 | 1 1 2 1
.o3.o3.o4.o | * 96 | 0 0 4 2 | 0 0 0 2 4 2 1 | 0 1 2 2
----------------+--------+----------------+------------------------+-----------
.. x. .. .. | 2 0 | 192 * * * | 1 1 0 0 1 0 0 | 1 0 1 1
.. .. .. x. | 2 0 | * 192 * * | 0 1 1 0 0 1 0 | 1 1 1 0
oo3oo3oo4oo&#x | 1 1 | * * 384 * | 0 0 0 1 1 1 0 | 0 1 1 1
.. .x .. .. | 0 2 | * * * 96 | 0 0 0 0 2 0 1 | 0 0 1 2
----------------+--------+----------------+------------------------+-----------
.. x.3o. .. | 3 0 | 3 0 0 0 | 64 * * * * * * | 1 0 0 1
.. x. .. x. | 4 0 | 2 2 0 0 | * 96 * * * * * | 1 0 1 0
.. .. o.4x. | 4 0 | 0 4 0 0 | * * 48 * * * * | 1 1 0 0
qo .. oq ..&#zx | 2 2 | 0 0 4 0 | * * * 96 * * * | 0 1 0 1
.. xx .. ..&#x | 2 2 | 1 0 2 1 | * * * * 192 * * | 0 0 1 1
.. .. .. xo&#x | 2 1 | 0 1 2 0 | * * * * * 192 * | 0 1 1 0
.o3.x .. .. | 0 3 | 0 0 0 3 | * * * * * * 32 | 0 0 0 2
----------------+--------+----------------+------------------------+-----------
.. x.3o.4x. | 24 0 | 24 24 0 0 | 8 12 6 0 0 0 0 | 8 * * * sirco
qo .. oq4xo&#zx | 8 4 | 0 8 16 0 | 0 0 2 4 0 8 0 | * 24 * * co
.. xx .. xo&#x | 4 2 | 2 2 4 1 | 0 1 0 0 2 2 0 | * * 96 * trip
qo3xx3oq ..&#zx | 12 12 | 12 0 24 12 | 4 0 0 6 12 0 4 | * * * 16 sirco
which obviously is nothing but srico (o3x4o3x). - (Thus this addition of .. xx .. .. in that o3o34o subsymmetry corresponds to the addition of . . . x in o3o4o3o symmetry.)
Then we add again xx .. .. .. to the above. This results in
wx3xx3oq4xo&#zx:
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wx3xx3oq4xo&#zx -> height = 0
o.3o.3o.4o. | 192 * | 2 2 2 0 0 | 1 2 1 1 2 2 0 | 1 1 1 2
.o3.o3.o4.o | * 192 | 0 0 2 1 1 | 0 0 0 2 2 1 1 | 0 2 1 1
----------------+---------+-------------------+------------------------+-----------
.. x. .. .. | 2 0 | 192 * * * * | 1 1 0 0 1 0 0 | 1 1 0 1
.. .. .. x. | 2 0 | * 192 * * * | 0 1 1 0 0 1 0 | 1 0 1 1
oo3oo3oo4oo&#x | 1 1 | * * 384 * * | 0 0 0 1 1 1 0 | 0 1 1 1
.x .. .. .. | 0 2 | * * * 96 * | 0 0 0 2 0 0 1 | 0 2 1 0
.. .x .. .. | 0 2 | * * * * 96 | 0 0 0 0 2 0 1 | 0 2 0 1
----------------+---------+-------------------+------------------------+-----------
.. x.3o. .. | 3 0 | 3 0 0 0 0 | 64 * * * * * * | 1 1 0 0
.. x. .. x. | 4 0 | 2 2 0 0 0 | * 96 * * * * * | 1 0 0 1
.. .. o.4x. | 4 0 | 0 4 0 0 0 | * * 48 * * * * | 1 0 1 0
wx .. oq ..&#zx | 2 4 | 0 0 4 2 0 | * * * 96 * * * | 0 1 1 0 non-regular 90-135-135-90-135-135 hexagons!!!
.. xx .. ..&#x | 2 2 | 1 0 2 0 1 | * * * * 192 * * | 0 1 0 1
.. .. .. xo&#x | 2 1 | 0 1 2 0 0 | * * * * * 192 * | 0 0 1 1
.x3.x .. .. | 0 6 | 0 0 0 3 3 | * * * * * * 32 | 0 2 0 0
----------------+---------+-------------------+------------------------+-----------
.. x.3o.4x. | 24 0 | 24 24 0 0 0 | 8 12 6 0 0 0 0 | 8 * * * sirco
wx3xx3oq ..&#zx | 12 24 | 12 0 24 12 12 | 4 0 0 6 12 0 4 | * 16 * * non-CRF tetrahedrally-lowered sirco (4)
wx .. oq4xo&#zx | 8 8 | 0 8 16 4 0 | 0 0 2 4 0 8 0 | * * 24 * non-CRF tetragonal-elongated cuboctahedron (2)
.. xx .. xo&#x | 4 2 | 2 2 4 0 1 | 0 1 0 0 2 2 0 | * * * 96 trip
Alternatively we could add .. .. xx .. to the today starting figure, resulting in
qo3xx3xw4xo&#zx:
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qo3xx3xw4xo&#zx -> height = 0
o.3o.3o.4o. | 384 * | 1 1 1 1 0 | 1 1 1 1 1 1 0 | 1 1 1 1
.o3.o3.o4.o | * 96 | 0 0 0 4 2 | 0 0 0 2 4 2 1 | 0 2 1 2
----------------+--------+--------------------+------------------------+-----------
.. x. .. .. | 2 0 | 192 * * * * | 1 1 0 0 1 0 0 | 1 1 0 1
.. .. x. .. | 2 0 | * 192 * * * | 1 0 1 1 0 0 0 | 1 1 1 0
.. .. .. x. | 2 0 | * * 192 * * | 0 1 1 0 0 1 0 | 1 0 1 1
oo3oo3oo4oo&#x | 1 1 | * * * 384 * | 0 0 0 1 1 1 0 | 0 1 1 1
.. .x .. .. | 0 2 | * * * * 96 | 0 0 0 0 2 0 1 | 0 2 0 1
----------------+--------+--------------------+------------------------+-----------
.. x.3x. .. | 6 0 | 3 3 0 0 0 | 64 * * * * * * | 1 1 0 0
.. x. .. x. | 4 0 | 2 0 2 0 0 | * 96 * * * * * | 1 0 0 1
.. .. x.4x. | 8 0 | 0 4 4 0 0 | * * 48 * * * * | 1 0 1 0
qo .. xw ..&#zx | 4 2 | 0 2 0 4 0 | * * * 96 * * * | 0 1 1 0 non-regular 90-135-135-90-135-135 hexagons!!!
.. xx .. ..&#x | 2 2 | 1 0 0 2 1 | * * * * 192 * * | 0 1 0 1
.. .. .. xo&#x | 2 1 | 0 0 1 2 0 | * * * * * 192 * | 0 0 1 1
.o3.x .. .. | 0 3 | 0 0 0 0 3 | * * * * * * 32 | 0 2 0 0
----------------+--------+--------------------+------------------------+-----------
.. x.3x.4x. | 48 0 | 24 24 24 0 0 | 8 12 6 0 0 0 0 | 8 * * * girco
qo3xx3xw ..&#zx | 24 12 | 12 12 0 24 12 | 4 0 0 6 12 0 4 | * 16 * * non-CRF tetrahedrally-lowered sirco (4)
qo .. xw4xo&#zx | 16 4 | 0 8 8 16 0 | 0 0 2 4 0 8 0 | * * 24 * non-CRF axially-contracted truncated cube (3)
.. xx .. xo&#x | 4 2 | 2 0 2 4 1 | 0 1 0 0 2 2 0 | * * * 96 trip
Here (2) and (3) are again those CUE polyhedra mentioned yesterday.
(4) is also a CUE polyhedron. It can be derived from sirco (x3o4x), when a tetrahedral subset of triangles becomes lowered. Thereby These triangles become regular hexagons (while the other tetrahedral subset of triangles remains as is). The squares in cubical positions become those non-regular hexagons, and the lacing squares (after some rescaling) also remain as is.
Finally we can have all 3 Stott expansions simultanuously. This then results in
wx3xx3xw4xo&#zx:
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wx3xx3xw4xo&#zx -> height = 0
o.3o.3o.4o. | 384 * | 1 1 1 1 0 0 | 1 1 1 1 1 1 0 | 1 1 1 1
.o3.o3.o4.o | * 192 | 0 0 0 2 1 1 | 0 0 0 2 2 1 1 | 0 2 1 1
----------------+---------+-----------------------+------------------------+-----------
.. x. .. .. | 2 0 | 192 * * * * * | 1 1 0 0 1 0 0 | 1 1 0 1
.. .. x. .. | 2 0 | * 192 * * * * | 1 0 1 1 0 0 0 | 1 1 1 0
.. .. .. x. | 2 0 | * * 192 * * * | 0 1 1 0 0 1 0 | 1 0 1 1
oo3oo3oo4oo&#x | 1 1 | * * * 384 * * | 0 0 0 1 1 1 0 | 0 1 1 1
.x .. .. .. | 0 2 | * * * * 96 * | 0 0 0 2 0 0 1 | 0 2 1 0
.. .x .. .. | 0 2 | * * * * * 96 | 0 0 0 0 2 0 1 | 0 2 0 1
----------------+---------+-----------------------+------------------------+-----------
.. x.3x. .. | 6 0 | 3 3 0 0 0 0 | 64 * * * * * * | 1 1 0 0
.. x. .. x. | 4 0 | 2 0 2 0 0 0 | * 96 * * * * * | 1 0 0 1
.. .. x.4x. | 8 0 | 0 4 4 0 0 0 | * * 48 * * * * | 1 0 1 0
wx .. xw ..&#zx | 4 4 | 0 2 0 4 2 0 | * * * 96 * * * | 0 1 1 0
.. xx .. ..&#x | 2 2 | 1 0 0 2 0 1 | * * * * 192 * * | 0 1 0 1
.. .. .. xo&#x | 2 1 | 0 0 1 2 0 0 | * * * * * 192 * | 0 0 1 1
.x3.x .. .. | 0 6 | 0 0 0 0 3 3 | * * * * * * 32 | 0 2 0 0
----------------+---------+-----------------------+------------------------+-----------
.. x.3x.4x. | 48 0 | 24 24 24 0 0 0 | 8 12 6 0 0 0 0 | 8 * * * girco
wx3xx3xw ..&#zx | 24 24 | 12 12 0 24 12 12 | 4 0 0 6 12 0 4 | * 16 * * girco
wx .. xw4xo&#zx | 16 8 | 0 8 8 16 4 0 | 0 0 2 4 0 8 0 | * * 24 * tic
.. xx .. xo&#x | 4 2 | 2 0 2 4 0 1 | 0 1 0 0 2 2 0 | * * * 96 trip
which thus happens to be Wythoffian again: it is nothing but grico (o3x4x3x), again the corresponding expansion of cont (o3x4x3o) wrt. to full o3o4o3o symmetry, as mentioned above.
Thus we have figured out here 2 more (i.e. in total 4)
CUE polychora, all being related to that single
CUE polygon, the 90-135-135-90-135-135 degrees Hexagon (in the following pic marked 'H'). And we found now a total 4 corresponding
CUE polyhedra as well:
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(1) tetrahedrally (2) fourfold- (3) fourfold- (4) tetrahedrally
truncated axially contracted lowered
cube elongated truncated small rhombi-
cuboctahedron cube cuboctahedron
H 4 8 H
+-----+---+ +---+---+ +---+-----+---+ +-----+---+
| \ | | / \ | | / \ | / | 4 | \
| + + + H + H + H +---+-----+ 6 +
H + H | H H | H | H | \ / | | 4 | \ |
| \ | + + +---+-----+---+ | | +---+
+---+-----+ | \ / | 8 H +---+ H | | H
H +---+---+ | \ | 4 |
4 + 6 +-----+---+
\ | 4 | /
+---+-----+
H
--- rk