Acronym chon Name cubic honeycomb,3D hypercubical honeycomb (δ3),Voronoi complex of primitive cubical lattice,Delone complex of primitive cubical lattice ` ©` Vertex figure ` ©` Dual (selfdual) Confer related tesselations: Voronoi complex of bcc lattice   Delone complex of fcc lattice   general polytopal classes: hypercubical honeycomb Externallinks

The Voronoi complex and the Delone complex of the primitive cubic lattice are relatively shifted copies of this cubic honeycomb.

Incidence matrix according to Dynkin symbol

```x4o3o4o   (N→∞)

. . . . | N ♦  6 | 12 | 8
--------+---+----+----+--
x . . . | 2 | 3N |  4 | 4
--------+---+----+----+--
x4o . . | 4 |  4 | 3N | 2
--------+---+----+----+--
x4o3o . ♦ 8 | 12 |  6 | N
```

```x4o3o4x   (N→∞)

. . . . | 8N ♦   3   3 |  3   6  3 | 1  3  3 1
--------+----+---------+-----------+----------
x . . . |  2 | 12N   * |  2   2  0 | 1  2  1 0
. . . x |  2 |   * 12N |  0   2  2 | 0  1  2 1
--------+----+---------+-----------+----------
x4o . . |  4 |   4   0 | 6N   *  * | 1  1  0 0
x . . x |  4 |   2   2 |  * 12N  * | 0  1  1 0
. . o4x |  4 |   0   4 |  *   * 6N | 0  0  1 1
--------+----+---------+-----------+----------
x4o3o . ♦  8 |  12   0 |  6   0  0 | N  *  * *
x4o . x ♦  8 |   8   4 |  2   4  0 | * 3N  * *
x . o4x ♦  8 |   4   8 |  0   4  2 | *  * 3N *
. o3o4x ♦  8 |   0  12 |  0   0  6 | *  *  * N
```

```o3o3o *b4x   (N→∞)

. . .    . | 2N ♦  6 | 12 | 4 4
-----------+----+----+----+----
. . .    x |  2 | 6N |  4 | 2 2
-----------+----+----+----+----
. o . *b4x |  4 |  4 | 6N | 1 1
-----------+----+----+----+----
o3o . *b4x ♦  8 | 12 |  6 | N *
. o3o *b4x ♦  8 | 12 |  6 | * N
```

```x∞o x4o4o   (N→∞)

. . . . . | N ♦ 2  4 |  8 4 | 8
----------+---+------+------+--
x . . . . | 2 | N  * |  4 0 | 4
. . x . . | 2 | * 2N |  2 2 | 4
----------+---+------+------+--
x . x . . | 4 | 2  2 | 2N * | 2
. . x4o . | 4 | 0  4 |  * N | 2
----------+---+------+------+--
x . x4o . ♦ 8 | 4  8 |  4 2 | N
```

```x∞o o4x4o   (N→∞)

. . . . . | 2N ♦  2  4 |  8 2 2 | 4 4
----------+----+-------+--------+----
x . . . . |  2 | 2N  * |  4 0 0 | 2 2
. . . x . |  2 |  * 4N |  2 1 1 | 2 2
----------+----+-------+--------+----
x . . x . |  4 |  2  2 | 4N * * | 1 1
. . o4x . |  4 |  0  4 |  * N * | 2 0
. . . x4o |  4 |  0  4 |  * * N | 0 2
----------+----+-------+--------+----
x . o4x . ♦  8 |  4  8 |  4 2 0 | N *
x . . x4o ♦  8 |  4  8 |  4 0 2 | * N
```

```x∞o x4o4x   (N→∞)

. . . . . | 4N ♦  2  2  2 |  4  4 1  2 1 | 2  4 2
----------+----+----------+--------------+-------
x . . . . |  2 | 4N  *  * |  2  2 0  0 0 | 1  2 1
. . x . . |  2 |  * 4N  * |  2  0 1  1 0 | 2  2 0
. . . . x |  2 |  *  * 4N |  0  2 0  1 1 | 0  2 2
----------+----+----------+--------------+-------
x . x . . |  4 |  2  2  0 | 4N  * *  * * | 1  1 0
x . . . x |  4 |  2  0  2 |  * 4N *  * * | 0  1 1
. . x4o . |  4 |  0  4  0 |  *  * N  * * | 2  0 0
. . x . x |  4 |  0  2  2 |  *  * * 2N * | 0  2 0
. . . o4x |  4 |  0  0  4 |  *  * *  * N | 0  0 2
----------+----+----------+--------------+-------
x . x4o . ♦  8 |  4  8  0 |  4  0 2  0 0 | N  * *
x . x . x ♦  8 |  4  4  4 |  2  2 0  2 0 | * 2N *
x . . o4x ♦  8 |  4  0  8 |  0  4 0  0 2 | *  * N
```

```x∞x x4o4o   (N→∞)

. . . . . | 2N ♦ 1 1  4 |  4  4  4 | 4 4
----------+----+--------+----------+----
x . . . . |  2 | N *  * |  4  0  0 | 4 0
. x . . . |  2 | * N  * |  4  0  0 | 0 4
. . x . . |  2 | * * 4N |  1  1  2 | 2 2
----------+----+--------+----------+----
x . x . . |  4 | 2 0  2 | 2N  *  * | 2 0
. x x . . |  4 | 0 2  2 |  * 2N  * | 0 2
. . x4o . |  4 | 0 0  4 |  *  * 2N | 1 1
----------+----+--------+----------+----
x . x4o . ♦  8 | 4 0  8 |  4  0  2 | N
. x x4o . ♦  8 | 0 4  8 |  0  4  2 | N
```

```x∞x o4x4o   (N→∞)

. . . . . | 4N ♦  1  1  4 |  4  4  2  2 | 2 2 2 2
----------+----+----------+-------------+--------
x . . . . |  2 | 2N  *  * |  4  0  0  0 | 2 2 0 0
. x . . . |  2 |  * 2N  * |  0  4  0  0 | 0 0 2 2
. . . x . |  2 |  *  * 8N |  1  1  1  1 | 1 1 1 1
----------+----+----------+-------------+--------
x . . x . |  4 |  2  0  2 | 4N  *  *  * | 1 1 0 0
. x . x . |  4 |  0  2  2 |  * 4N  *  * | 0 0 1 1
. . o4x . |  4 |  0  0  4 |  *  * 2N  * | 1 0 1 0
. . . x4o |  4 |  0  0  4 |  *  *  * 2N | 0 1 0 1
----------+----+----------+-------------+--------
x . o4x . ♦  8 |  4  0  8 |  4  0  2  0 | N * * *
x . . x4o ♦  8 |  4  0  8 |  4  0  0  2 | * N * *
. x o4x . ♦  8 |  0  4  8 |  0  4  2  0 | * * N *
. x . x4o ♦  8 |  0  4  8 |  0  4  0  2 | * * * N
```

```x∞x x4o4x   (N→∞)

. . . . . | 8N ♦  1  1  2  2 |  2  2  2  2  1  2  1 | 1  2 1 1  2 1
----------+----+-------------+----------------------+--------------
x . . . . |  2 | 4N  *  *  * |  2  2  0  0  0  0  0 | 1  2 1 0  0 0
. x . . . |  2 |  * 4N  *  * |  0  0  2  2  0  0  0 | 0  0 0 1  2 1
. . x . . |  2 |  *  * 8N  * |  1  0  1  0  1  1  0 | 1  1 0 1  1 0
. . . . x |  2 |  *  *  * 8N |  0  1  0  1  0  1  1 | 0  1 1 0  1 1
----------+----+-------------+----------------------+--------------
x . x . . |  4 |  2  0  2  0 | 4N  *  *  *  *  *  * | 1  1 0 0  0 0
x . . . x |  4 |  2  0  0  2 |  * 4N  *  *  *  *  * | 0  1 1 0  0 0
. x x . . |  4 |  0  2  2  0 |  *  * 4N  *  *  *  * | 0  0 0 1  1 0
. x . . x |  4 |  0  2  0  2 |  *  *  * 4N  *  *  * | 0  0 0 0  1 1
. . x4o . |  4 |  0  0  4  0 |  *  *  *  * 2N  *  * | 1  0 0 1  0 0
. . x . x |  4 |  0  0  2  2 |  *  *  *  *  * 4N  * | 0  1 0 0  1 0
. . . o4x |  4 |  0  0  0  4 |  *  *  *  *  *  * 2N | 0  0 1 0  0 1
----------+----+-------------+----------------------+--------------
x . x4o . ♦  8 |  4  0  8  0 |  4  0  0  0  2  0  0 | N  * * *  * *
x . x . x ♦  8 |  4  0  4  4 |  2  2  0  0  0  2  0 | * 2N * *  * *
x . . o4x ♦  8 |  4  0  0  8 |  0  4  0  0  0  0  2 | *  * N *  * *
. x x4o . ♦  8 |  0  4  8  0 |  0  0  4  0  2  0  0 | *  * * N  * *
. x x . x ♦  8 |  0  4  4  4 |  0  0  2  2  0  2  0 | *  * * * 2N *
. x . o4x ♦  8 |  0  4  0  8 |  0  0  0  4  0  0  2 | *  * * *  * N
```

```x∞o x∞o x∞o (N→∞)

. . . . . . | N ♦ 2 2 2 | 4 4 4 | 8
------------+---+-------+-------+--
x . . . . . | 2 | N * * | 2 2 0 | 4
. . x . . . | 2 | * N * | 2 0 2 | 4
. . . . x . | 2 | * * N | 0 2 2 | 4
------------+---+-------+-------+--
x . x . . . | 4 | 2 2 0 | N * * | 2
x . . . x . | 4 | 2 0 2 | * N * | 2
. . x . x . | 4 | 0 2 2 | * * N | 2
------------+---+-------+-------+--
x . x . x . ♦ 8 | 4 4 4 | 2 2 2 | N
```

```x∞x x∞o x∞o (N→∞)

. . . . . . | 2N ♦ 1 1  2  2 | 2 2 2 2  4 | 4 4
------------+----+-----------+------------+----
x . . . . . |  2 | N *  *  * | 2 2 0 0  0 | 4 0
. x . . . . |  2 | * N  *  * | 0 0 2 2  0 | 0 4
. . x . . . |  2 | * * 2N  * | 1 0 1 0  2 | 2 2
. . . . x . |  2 | * *  * 2N | 0 1 0 1  2 | 2 2
------------+----+-----------+------------+----
x . x . . . |  4 | 2 0  2  0 | N * * *  * | 2 0
x . . . x . |  4 | 2 0  0  2 | * N * *  * | 2 0
. x x . . . |  4 | 0 2  2  0 | * * N *  * | 0 2
. x . . x . |  4 | 0 2  0  2 | * * * N  * | 0 2
. . x . x . |  4 | 0 0  2  2 | * * * * 2N | 1 1
------------+----+-----------+------------+----
x . x . x . ♦  8 | 4 0  4  4 | 2 2 0 0  2 | N *
. x x . x . ♦  8 | 0 4  4  4 | 0 0 2 2  2 | * N
```

```x∞x x∞x x∞o (N→∞)

. . . . . . | 4N ♦  1  1  1  1  2 | 1 1  2 1 1  2  2  2 | 2 2 2 2
------------+----+----------------+---------------------+--------
x . . . . . |  2 | 2N  *  *  *  * | 1 1  2 0 0  0  0  0 | 2 2 0 0
. x . . . . |  2 |  * 2N  *  *  * | 0 0  0 1 1  2  0  0 | 0 0 2 2
. . x . . . |  2 |  *  * 2N  *  * | 1 0  0 1 0  0  2  0 | 2 0 2 0
. . . x . . |  2 |  *  *  * 2N  * | 0 1  0 0 1  0  0  2 | 0 2 0 2
. . . . x . |  2 |  *  *  *  * 4N | 0 0  1 0 0  1  1  1 | 1 1 1 1
------------+----+----------------+---------------------+--------
x . x . . . |  4 |  2  0  2  0  0 | N *  * * *  *  *  * | 2 0 0 0
x . . x . . |  4 |  2  0  0  2  0 | * N  * * *  *  *  * | 0 2 0 0
x . . . x . |  4 |  2  0  0  0  2 | * * 2N * *  *  *  * | 1 1 0 0
. x x . . . |  4 |  0  2  2  0  0 | * *  * N *  *  *  * | 0 0 2 0
. x . x . . |  4 |  0  2  0  2  0 | * *  * * N  *  *  * | 0 0 0 2
. x . . x . |  4 |  0  2  0  0  2 | * *  * * * 2N  *  * | 0 0 1 1
. . x . x . |  4 |  0  0  2  0  2 | * *  * * *  * 2N  * | 1 0 1 0
. . . x x . |  4 |  0  0  0  2  2 | * *  * * *  *  * 2N | 0 1 0 1
------------+----+----------------+---------------------+--------
x . x . x . ♦  8 |  4  0  4  0  4 | 2 0  2 0 0  0  2  0 | N * * *
x . . x x . ♦  8 |  4  0  0  4  4 | 0 2  2 0 0  0  0  2 | * N * *
. x x . x . ♦  8 |  0  4  4  0  4 | 0 0  0 2 0  2  2  0 | * * N *
. x . x x . ♦  8 |  0  4  0  4  4 | 0 0  0 0 2  2  0  2 | * * * N
```

```x∞x x∞x x∞x (N→∞)

. . . . . . | 8N ♦  1  1  1  1  1  1 |  1  1  1  1  1  1  1  1  1  1  1  1 | 1 1 1 1 1 1 1 1
------------+----+-------------------+-------------------------------------+----------------
x . . . . . |  2 | 4N  *  *  *  *  * |  1  1  1  1  0  0  0  0  0  0  0  0 | 1 1 1 1 0 0 0 0
. x . . . . |  2 |  * 4N  *  *  *  * |  0  0  0  0  1  1  1  1  0  0  0  0 | 0 0 0 0 1 1 1 1
. . x . . . |  2 |  *  * 4N  *  *  * |  1  0  0  0  1  0  0  0  1  1  0  0 | 1 1 0 0 1 1 0 0
. . . x . . |  2 |  *  *  * 4N  *  * |  0  1  0  0  0  1  0  0  0  0  1  1 | 0 0 1 1 0 0 1 1
. . . . x . |  2 |  *  *  *  * 4N  * |  0  0  1  0  0  0  1  0  1  0  1  0 | 1 0 1 0 1 0 1 0
. . . . . x |  2 |  *  *  *  *  * 4N |  0  0  0  1  0  0  0  1  0  1  0  1 | 0 1 0 1 0 1 0 1
------------+----+-------------------+-------------------------------------+----------------
x . x . . . |  4 |  2  0  2  0  0  0 | 2N  *  *  *  *  *  *  *  *  *  *  * | 1 1 0 0 0 0 0 0
x . . x . . |  4 |  2  0  0  2  0  0 |  * 2N  *  *  *  *  *  *  *  *  *  * | 0 0 1 1 0 0 0 0
x . . . x . |  4 |  2  0  0  0  2  0 |  *  * 2N  *  *  *  *  *  *  *  *  * | 1 0 1 0 0 0 0 0
x . . . . x |  4 |  2  0  0  0  0  2 |  *  *  * 2N  *  *  *  *  *  *  *  * | 0 1 0 1 0 0 0 0
. x x . . . |  4 |  0  2  2  0  0  0 |  *  *  *  * 2N  *  *  *  *  *  *  * | 0 0 0 0 1 1 0 0
. x . x . . |  4 |  0  2  0  2  0  0 |  *  *  *  *  * 2N  *  *  *  *  *  * | 0 0 0 0 0 0 1 1
. x . . x . |  4 |  0  2  0  0  2  0 |  *  *  *  *  *  * 2N  *  *  *  *  * | 0 0 0 0 1 0 1 0
. x . . . x |  4 |  0  2  0  0  0  2 |  *  *  *  *  *  *  * 2N  *  *  *  * | 0 0 0 0 0 1 0 1
. . x . x . |  4 |  0  0  2  0  2  0 |  *  *  *  *  *  *  *  * 2N  *  *  * | 1 0 0 0 1 0 0 0
. . x . . x |  4 |  0  0  2  0  0  2 |  *  *  *  *  *  *  *  *  * 2N  *  * | 0 1 0 0 0 1 0 0
. . . x x . |  4 |  0  0  0  2  2  0 |  *  *  *  *  *  *  *  *  *  * 2N  * | 0 0 1 0 0 0 1 0
. . . x . x |  4 |  0  0  0  2  0  2 |  *  *  *  *  *  *  *  *  *  *  * 2N | 0 0 0 1 0 0 0 1
------------+----+-------------------+-------------------------------------+----------------
x . x . x . ♦  8 |  4  0  4  0  4  0 |  2  0  2  0  0  0  0  0  2  0  0  0 | N * * * * * * *
x . x . . x ♦  8 |  4  0  4  0  0  4 |  2  0  0  2  0  0  0  0  0  2  0  0 | * N * * * * * *
x . . x x . ♦  8 |  4  0  0  4  4  0 |  0  2  2  0  0  0  0  0  0  0  2  0 | * * N * * * * *
x . . x . x ♦  8 |  4  0  0  4  0  4 |  0  2  0  2  0  0  0  0  0  0  0  2 | * * * N * * * *
. x x . x . ♦  8 |  0  4  4  0  4  0 |  0  0  0  0  2  0  2  0  2  0  0  0 | * * * * N * * *
. x x . . x ♦  8 |  0  4  4  0  0  4 |  0  0  0  0  2  0  0  2  0  2  0  0 | * * * * * N * *
. x . x x . ♦  8 |  0  4  0  4  4  0 |  0  0  0  0  0  2  2  0  0  0  2  0 | * * * * * * N *
. x . x . x ♦  8 |  0  4  0  4  0  4 |  0  0  0  0  0  2  0  2  0  0  0  2 | * * * * * * * N
```