Acronym	batatoh
Name	bitruncated alternated-cubic honeycomb, bitruncated tetrahedral-octahedral honeycomb, quarter cubic honeycomb
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Vertex figure	©
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This honeycomb also can be described as s4o3o4s', i.e. as sequential applications of alternated facetings, according to x4o3o4x → s4o3o4x (= x3o3o *b4x) → x3o3o *b4s' (cf. below).

Incidence matrix according to Dynkin symbol

x3x3o3o3*a   (N → ∞)

. . . .    | 4N |  3  3 |  6  3  3 | 3 3 1 1
-----------+----+-------+----------+--------
x . . .    |  2 | 6N  * |  2  2  0 | 1 2 1 0
. x . .    |  2 |  * 6N |  2  0  2 | 2 1 0 1
-----------+----+-------+----------+--------
x3x . .    |  6 |  3  3 | 4N  *  * | 1 1 0 0
x . . o3*a |  3 |  3  0 |  * 4N  * | 0 1 1 0
. x3o .    |  3 |  0  3 |  *  * 4N | 1 0 0 1
-----------+----+-------+----------+--------
x3x3o .    ♦ 12 |  6 12 |  4  0  4 | N * * *
x3x . o3*a ♦ 12 | 12  6 |  4  4  0 | * N * *
x . o3o3*a ♦  4 |  6  0 |  0  4  0 | * * N *
. x3o3o    ♦  4 |  0  6 |  0  0  4 | * * * N

or
. . . .       | 2N |  6 |  6  6 | 6 2
--------------+----+----+-------+----
x . . .     & |  2 | 6N |  2  2 | 3 1
--------------+----+----+-------+----
x3x . .       |  6 |  6 | 2N  * | 2 0
x . . o3*a  & |  3 |  3 |  * 4N | 1 1
--------------+----+----+-------+----
x3x3o .     & ♦ 12 | 18 |  4  4 | N *
x . o3o3*a  & ♦  4 |  6 |  0  4 | * N

x3x3o3/2o3/2*a   (N → ∞)

. . .   .      | 4N |  3  3 |  6  3  3 | 3 3 1 1
---------------+----+-------+----------+--------
x . .   .      |  2 | 6N  * |  2  2  0 | 1 2 1 0
. x .   .      |  2 |  * 6N |  2  0  2 | 2 1 0 1
---------------+----+-------+----------+--------
x3x .   .      |  6 |  3  3 | 4N  *  * | 1 1 0 0
x . .   o3/2*a |  3 |  3  0 |  * 4N  * | 0 1 1 0
. x3o   .      |  3 |  0  3 |  *  * 4N | 1 0 0 1
---------------+----+-------+----------+--------
x3x3o   .      ♦ 12 |  6 12 |  4  0  4 | N * * *
x3x .   o3/2*a ♦ 12 | 12  6 |  4  4  0 | * N * *
x . o3/2o3/2*a ♦  4 |  6  0 |  0  4  0 | * * N *
. x3o3/2o      ♦  4 |  0  6 |  0  0  4 | * * * N

x3o3o *b4s   (N → ∞)

demi( . . .    . ) | 4N |  3  3 |  3  6  3 | 1 3 1 3
-------------------+----+-------+----------+--------
demi( x . .    . ) |  2 | 6N  * |  2  2  0 | 1 2 0 1
      . o . *b4s   |  2 |  * 6N |  0  2  2 | 0 1 1 2
-------------------+----+-------+----------+--------
demi( x3o .    . ) |  3 |  3  0 | 4N  *  * | 1 1 0 0
sefa( x3o . *b4s ) |  6 |  3  3 |  * 4N  * | 0 1 0 1
sefa( . o3o *b4s ) |  3 |  0  3 |  *  * 4N | 0 0 1 1
-------------------+----+-------+----------+--------
demi( x3o3o    . ) ♦  4 |  6  0 |  4  0  0 | N * * *
      x3o . *b4s   ♦ 12 | 12  6 |  4  4  0 | * N * *
      . o3o *b4s   ♦  4 |  0  6 |  0  0  4 | * * N *
sefa( x3o3o *b4s ) ♦ 12 |  6 12 |  0  4  4 | * * * N

starting figure: x3o3o *b4x