Acronym ico
Name icositetrachoron,
24-cell,
xylochoron,
birectified tesseract

Cross sections
` ©`
Vertex figure
` ©`
Vertex layers
 Layer Symmetry Subsymmetries o3o4o3o o3o4o . o3o . o o . o3o . o4o3o 1 x3o4o3o x3o4o .oct first x3o . o{3} first x . o3oedge first . o4o3overtex first 2 o3x4o . o3x . q o . q3o . x4o3overtex figure 3 x3o4o .opposite oct x3x . o x . o3q . o4o3q 4 x3o . q u . o3o . x4o3o 5 o3x . oopposite {3} x . q3o . o4o3oopposite vertex 6 o . o3q 7 x . o3oopposite edge o3o3o4o o3o3o . o3o . o o . o4o . o3o4o 1 o3x3o4o o3x3o .oct first o3x . o{3} first o . o4overtex first . x3o4ooct first 2 x3o3x . x3o . q x . x4overtex figure . o3x4o 3a o3x3o .opposite oct x3x . o u . o4o . x3o4oopposite oct 3b o . o4q 4 o3x . q x . x4o 5 x3o . oopposite {3} o . o4oopposite vertex o3o3o *b3o o3o3o    . o3o . *b3o o . o    o . o3o *b3o 1 o3x3o *b3o o3x3o    .oct first o3x . *b3ooct first o . o    overtex first . x3o *b3ooct first 2 x3o3x    . x3o . *b3x x . x    xvertex figure . o3x *b3x 3a o3x3o    .opposite oct o3x . *b3oopposite oct u . o    o . x3o *b3oopposite oct 3b o . u    o 3c o . o    u 4 x . x    x 5 o . o    oopposite vertex
Lace city
in approx. ASCII-art
 ``` ©   ``` ``` o3o o3o q3o o3q o3o o3q q3o o3o q3o o3q o3o o3o ```
 ``` ©   ``` ``` o3x x3o x3o x3x o3x o3x x3o ```
 ``` ©   ``` ```o4o x4o o4o x4o o4q x4o o4o x4o o4o ```
Coordinates
1. (1, 0, 0, 0)                & all permutations, all changes of sign
(vertex inscribed 1/q-hex)
2. (1/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
(vertex inscribed tes)
• or just   (1/sqrt(2), 1/sqrt(2), 0, 0)   & all permutations, all changes of sign
(in dual positioning)
• (the compound of those 2 such oriented icositetrachora is stoc)
General of army (is itself convex)
Colonel of regiment (is itself locally convex
 by cells: cho co cube oct oho thah hoh honho 8 4 0 0 0 24 hohoh 8 0 0 8 0 16 huhoh 8 0 0 0 0 16 dod honho 4 4 0 0 4 16 hodho 4 0 0 16 4 8 odho 4 0 0 0 4 8 ihi 0 12 0 0 0 24 ohuhoh 0 8 0 8 0 16 ghahoh 0 8 0 0 0 16 doh honho 0 4 0 8 8 8 ratho 0 4 0 8 0 8 gico (compound) 0 0 24 0 0 0 ico 0 0 0 24 0 0 shahoh 0 0 0 16 8 0 oh 0 0 0 8 8 0
)
Dual (selfdual, in different orientation)
Confer
Grünbaumian relatives:
2ico   2ico+48{4}+128{3}   2ico+2gico   ico+gico+72{4}   ico+gico+24co
compounds:
stoc   chi   dox
segmentochora:
oct || co   {6} || oct   cubpy
uniform relative:
hex   tes
general polytopal classes:
regular
External

As can be seen from what is mentioned above (at coordinates): the hex-diminished ico is nothing but the tes. Conversely, the 8-diminished ico (corresponding to the vertex directions of tes) is nothing but the hex.

Incidence matrix according to Dynkin symbol

```x3o4o3o

. . . . | 24 ♦  8 | 12 |  6
--------+----+----+----+---
x . . . |  2 | 96 |  3 |  3
--------+----+----+----+---
x3o . . |  3 |  3 | 96 |  2
--------+----+----+----+---
x3o4o . ♦  6 | 12 |  8 | 24
```

```x3o4o3/2o

. . .   . | 24 ♦  8 | 12 |  6
----------+----+----+----+---
x . .   . |  2 | 96 |  3 |  3
----------+----+----+----+---
x3o .   . |  3 |  3 | 96 |  2
----------+----+----+----+---
x3o4o   . ♦  6 | 12 |  8 | 24
```

```x3o4/3o3o

. .   . . | 24 ♦  8 | 12 |  6
----------+----+----+----+---
x .   . . |  2 | 96 |  3 |  3
----------+----+----+----+---
x3o   . . |  3 |  3 | 96 |  2
----------+----+----+----+---
x3o4/3o . ♦  6 | 12 |  8 | 24
```

```x3o4/3o3/2o

. .   .   . | 24 ♦  8 | 12 |  6
------------+----+----+----+---
x .   .   . |  2 | 96 |  3 |  3
------------+----+----+----+---
x3o   .   . |  3 |  3 | 96 |  2
------------+----+----+----+---
x3o4/3o   . ♦  6 | 12 |  8 | 24
```

```x3/2o4o3o

.   . . . | 24 ♦  8 | 12 |  6
----------+----+----+----+---
x   . . . |  2 | 96 |  3 |  3
----------+----+----+----+---
x3/2o . . |  3 |  3 | 96 |  2
----------+----+----+----+---
x3/2o4o . ♦  6 | 12 |  8 | 24
```

```x3/2o4o3/2o

.   . .   . | 24 ♦  8 | 12 |  6
------------+----+----+----+---
x   . .   . |  2 | 96 |  3 |  3
------------+----+----+----+---
x3/2o .   . |  3 |  3 | 96 |  2
------------+----+----+----+---
x3/2o4o   . ♦  6 | 12 |  8 | 24
```

```x3/2o4/3o3o

.   .   . . | 24 ♦  8 | 12 |  6
------------+----+----+----+---
x   .   . . |  2 | 96 |  3 |  3
------------+----+----+----+---
x3/2o   . . |  3 |  3 | 96 |  2
------------+----+----+----+---
x3/2o4/3o . ♦  6 | 12 |  8 | 24
```

```x3/2o4/3o3/2o

.   .   .   . | 24 ♦  8 | 12 |  6
--------------+----+----+----+---
x   .   .   . |  2 | 96 |  3 |  3
--------------+----+----+----+---
x3/2o   .   . |  3 |  3 | 96 |  2
--------------+----+----+----+---
x3/2o4/3o   . ♦  6 | 12 |  8 | 24
```

```o3x3o4o

. . . . | 24 ♦  8 |  4  8 |  4 2
--------+----+----+-------+-----
. x . . |  2 | 96 |  1  2 |  2 1
--------+----+----+-------+-----
o3x . . |  3 |  3 | 32  * |  2 0
. x3o . |  3 |  3 |  * 64 |  1 1
--------+----+----+-------+-----
o3x3o . ♦  6 | 12 |  4  4 | 16 *
. x3o4o ♦  6 | 12 |  0  8 |  * 8
```

```o3x3o4/3o

. . .   . | 24 ♦  8 |  4  8 |  4 2
----------+----+----+-------+-----
. x .   . |  2 | 96 |  1  2 |  2 1
----------+----+----+-------+-----
o3x .   . |  3 |  3 | 32  * |  2 0
. x3o   . |  3 |  3 |  * 64 |  1 1
----------+----+----+-------+-----
o3x3o   . ♦  6 | 12 |  4  4 | 16 *
. x3o4/3o ♦  6 | 12 |  0  8 |  * 8
```

```o3x3/2o4o

. .   . . | 24 ♦  8 |  4  8 |  4 2
----------+----+----+-------+-----
. x   . . |  2 | 96 |  1  2 |  2 1
----------+----+----+-------+-----
o3x   . . |  3 |  3 | 32  * |  2 0
. x3/2o . |  3 |  3 |  * 64 |  1 1
----------+----+----+-------+-----
o3x3/2o . ♦  6 | 12 |  4  4 | 16 *
. x3/2o4o ♦  6 | 12 |  0  8 |  * 8
```

```o3x3/2o4/3o

. .   .   . | 24 ♦  8 |  4  8 |  4 2
------------+----+----+-------+-----
. x   .   . |  2 | 96 |  1  2 |  2 1
------------+----+----+-------+-----
o3x   .   . |  3 |  3 | 32  * |  2 0
. x3/2o   . |  3 |  3 |  * 64 |  1 1
------------+----+----+-------+-----
o3x3/2o   . ♦  6 | 12 |  4  4 | 16 *
. x3/2o4/3o ♦  6 | 12 |  0  8 |  * 8
```

```o3/2x3o4o

.   . . . | 24 ♦  8 |  4  8 |  4 2
----------+----+----+-------+-----
.   x . . |  2 | 96 |  1  2 |  2 1
----------+----+----+-------+-----
o3/2x . . |  3 |  3 | 32  * |  2 0
.   x3o . |  3 |  3 |  * 64 |  1 1
----------+----+----+-------+-----
o3/2x3o . ♦  6 | 12 |  4  4 | 16 *
.   x3o4o ♦  6 | 12 |  0  8 |  * 8
```

```o3/2x3o4/3o

.   . .   . | 24 ♦  8 |  4  8 |  4 2
------------+----+----+-------+-----
.   x .   . |  2 | 96 |  1  2 |  2 1
------------+----+----+-------+-----
o3/2x .   . |  3 |  3 | 32  * |  2 0
.   x3o   . |  3 |  3 |  * 64 |  1 1
------------+----+----+-------+-----
o3/2x3o   . ♦  6 | 12 |  4  4 | 16 *
.   x3o4/3o ♦  6 | 12 |  0  8 |  * 8
```

```o3/2x3/2o4o

.   .   . . | 24 ♦  8 |  4  8 |  4 2
------------+----+----+-------+-----
.   x   . . |  2 | 96 |  1  2 |  2 1
------------+----+----+-------+-----
o3/2x   . . |  3 |  3 | 32  * |  2 0
.   x3/2o . |  3 |  3 |  * 64 |  1 1
------------+----+----+-------+-----
o3/2x3/2o . ♦  6 | 12 |  4  4 | 16 *
.   x3/2o4o ♦  6 | 12 |  0  8 |  * 8
```

```o3/2x3/2o4/3o

.   .   .   . | 24 ♦  8 |  4  8 |  4 2
--------------+----+----+-------+-----
.   x   .   . |  2 | 96 |  1  2 |  2 1
--------------+----+----+-------+-----
o3/2x   .   . |  3 |  3 | 32  * |  2 0
.   x3/2o   . |  3 |  3 |  * 64 |  1 1
--------------+----+----+-------+-----
o3/2x3/2o   . ♦  6 | 12 |  4  4 | 16 *
.   x3/2o4/3o ♦  6 | 12 |  0  8 |  * 8
```

```o3x3o *b3o

. . .    . | 24 ♦  8 |  4  4  4 | 2 2 2
-----------+----+----+----------+------
. x .    . |  2 | 96 |  1  1  1 | 1 1 1
-----------+----+----+----------+------
o3x .    . |  3 |  3 | 32  *  * | 1 1 0
. x3o    . |  3 |  3 |  * 32  * | 1 0 1
. x . *b3o |  3 |  3 |  *  * 32 | 0 1 1
-----------+----+----+----------+------
o3x3o    . ♦  6 | 12 |  4  4  0 | 8 * *
o3x . *b3o ♦  6 | 12 |  4  0  4 | * 8 *
. x3o *b3o ♦  6 | 12 |  0  4  4 | * * 8
```

```o3x3o *b3/2o

. . .      . | 24 ♦  8 |  4  4  4 | 2 2 2
-------------+----+----+----------+------
. x .      . |  2 | 96 |  1  1  1 | 1 1 1
-------------+----+----+----------+------
o3x .      . |  3 |  3 | 32  *  * | 1 1 0
. x3o      . |  3 |  3 |  * 32  * | 1 0 1
. x . *b3/2o |  3 |  3 |  *  * 32 | 0 1 1
-------------+----+----+----------+------
o3x3o      . ♦  6 | 12 |  4  4  0 | 8 * *
o3x . *b3/2o ♦  6 | 12 |  4  0  4 | * 8 *
. x3o *b3/2o ♦  6 | 12 |  0  4  4 | * * 8
```

```o3x3/2o *b3/2o

. .   .      . | 24 ♦  8 |  4  4  4 | 2 2 2
---------------+----+----+----------+------
. x   .      . |  2 | 96 |  1  1  1 | 1 1 1
---------------+----+----+----------+------
o3x   .      . |  3 |  3 | 32  *  * | 1 1 0
. x3/2o      . |  3 |  3 |  * 32  * | 1 0 1
. x   . *b3/2o |  3 |  3 |  *  * 32 | 0 1 1
---------------+----+----+----------+------
o3x3/2o      . ♦  6 | 12 |  4  4  0 | 8 * *
o3x   . *b3/2o ♦  6 | 12 |  4  0  4 | * 8 *
. x3/2o *b3/2o ♦  6 | 12 |  0  4  4 | * * 8
```

```o3/2x3/2o *b3/2o

.   .   .      . | 24 ♦  8 |  4  4  4 | 2 2 2
-----------------+----+----+----------+------
.   x   .      . |  2 | 96 |  1  1  1 | 1 1 1
-----------------+----+----+----------+------
o3/2x   .      . |  3 |  3 | 32  *  * | 1 1 0
.   x3/2o      . |  3 |  3 |  * 32  * | 1 0 1
.   x   . *b3/2o |  3 |  3 |  *  * 32 | 0 1 1
-----------------+----+----+----------+------
o3/2x3/2o      . ♦  6 | 12 |  4  4  0 | 8 * *
o3/2x   . *b3/2o ♦  6 | 12 |  4  0  4 | * 8 *
.   x3/2o *b3/2o ♦  6 | 12 |  0  4  4 | * * 8
```

```xox3oxo4ooo&#xt   → both heights = 1/sqrt(2) = 0.707107
(oct || pseudo co || oct)

o..3o..4o..     | 6  * * ♦  4  4  0  0  0 | 4  4  4 0  0  0 0 | 1 4 1 0 0
.o.3.o.4.o.     | * 12 * ♦  0  2  4  2  0 | 0  1  4 2  4  1 0 | 0 2 2 2 0
..o3..o4..o     | *  * 6 ♦  0  0  0  4  4 | 0  0  0 0  4  4 4 | 0 0 1 4 1
----------------+--------+----------------+-------------------+----------
x.. ... ...     | 2  0 0 | 12  *  *  *  * | 2  1  0 0  0  0 0 | 1 2 0 0 0
oo.3oo.4oo.&#x  | 1  1 0 |  * 24  *  *  * | 0  1  2 0  0  0 0 | 0 2 1 0 0
... .x. ...     | 0  2 0 |  *  * 24  *  * | 0  0  1 1  1  0 0 | 0 1 1 1 0
.oo3.oo4.oo&#x  | 0  1 1 |  *  *  * 24  * | 0  0  0 0  2  1 0 | 0 0 1 2 0
..x ... ...     | 0  0 2 |  *  *  *  * 12 | 0  0  0 0  0  1 2 | 0 0 0 2 1
----------------+--------+----------------+-------------------+----------
x..3o.. ...     | 3  0 0 |  3  0  0  0  0 | 8  *  * *  *  * * | 1 1 0 0 0
xo. ... ...&#x  | 2  1 0 |  1  2  0  0  0 | * 12  * *  *  * * | 0 2 0 0 0
... ox. ...&#x  | 1  2 0 |  0  2  1  0  0 | *  * 24 *  *  * * | 0 1 1 0 0
.o.3.x. ...     | 0  3 0 |  0  0  3  0  0 | *  *  * 8  *  * * | 0 1 0 1 0
... .xo ...&#x  | 0  2 1 |  0  0  1  2  0 | *  *  * * 24  * * | 0 0 1 1 0
.ox ... ...&#x  | 0  1 2 |  0  0  0  2  1 | *  *  * *  * 12 * | 0 0 0 2 0
..x3..o ...     | 0  0 3 |  0  0  0  0  3 | *  *  * *  *  * 8 | 0 0 0 1 1
----------------+--------+----------------+-------------------+----------
x..3o..4o..     ♦ 6  0 0 | 12  0  0  0  0 | 8  0  0 0  0  0 0 | 1 * * * *
xo.3ox. ...&#x  ♦ 3  3 0 |  3  6  3  0  0 | 1  3  3 1  0  0 0 | * 8 * * *
... oxo4ooo&#xt ♦ 1  4 1 |  0  4  4  4  0 | 0  0  4 0  4  0 0 | * * 6 * *
.ox3.xo ...&#x  ♦ 0  3 3 |  0  0  3  6  3 | 0  0  0 1  3  3 1 | * * * 8 *
..x3..o4..o     ♦ 0  0 6 |  0  0  0  0 12 | 0  0  0 0  0  0 8 | * * * * 1

or
o..3o..4o..     & | 12  * ♦  4  4  0 |  4  4  4 0 | 1  4 1
.o.3.o.4.o.       |  * 12 ♦  0  4  4 |  0  2  8 2 | 0  4 2
------------------+-------+----------+------------+-------
x.. ... ...     & |  2  0 | 24  *  * |  2  1  0 0 | 1  2 0
oo.3oo.4oo.&#x  & |  1  1 |  * 48  * |  0  1  2 0 | 0  2 1
... .x. ...       |  0  2 |  *  * 24 |  0  0  2 1 | 0  2 1
------------------+-------+----------+------------+-------
x..3o.. ...     & |  3  0 |  3  0  0 | 16  *  * * | 1  1 0
xo. ... ...&#x  & |  2  1 |  1  2  0 |  * 24  * * | 0  2 0
... ox. ...&#x  & |  1  2 |  0  2  1 |  *  * 48 * | 0  1 1
.o.3.x. ...       |  0  3 |  0  0  3 |  *  *  * 8 | 0  2 0
------------------+-------+----------+------------+-------
x..3o..4o..     & ♦  6  0 | 12  0  0 |  8  0  0 0 | 2  * *
xo.3ox. ...&#x  & ♦  3  3 |  3  6  3 |  1  3  3 1 | * 16 *
... oxo4ooo&#xt   ♦  2  4 |  0  8  4 |  0  0  8 0 | *  * 6
```

```oxo3xox3oxo&#xt   → both heights = 1/sqrt(2) = 0.707107
(oct || pseudo co || oct)

o..3o..3o..     | 6  * * ♦  4  4  0  0  0  0 | 2 2  2  4  2 0 0  0  0  0 0 0 | 1 2 2 1 0 0 0
.o.3.o.3.o.     | * 12 * ♦  0  2  2  2  2  0 | 0 0  2  1  2 1 1  2  1  2 0 0 | 0 1 1 2 1 1 0
..o3..o3..o     | *  * 6 ♦  0  0  0  0  4  4 | 0 0  0  0  0 0 0  2  4  2 2 2 | 0 0 0 1 2 2 1
----------------+--------+-------------------+-------------------------------+--------------
... x.. ...     | 2  0 0 | 12  *  *  *  *  * | 1 1  0  1  0 0 0  0  0  0 0 0 | 1 1 1 0 0 0 0
oo. oo. oo.&#x  | 1  1 0 |  * 24  *  *  *  * | 0 0  1  1  1 0 0  0  0  0 0 0 | 0 1 1 1 0 0 0
.x. ... ...     | 0  2 0 |  *  * 12  *  *  * | 0 0  1  0  0 1 0  1  0  0 0 0 | 0 1 0 1 1 0 0
... ... .x.     | 0  2 0 |  *  *  * 12  *  * | 0 0  0  0  1 0 1  1  0  0 0 0 | 0 0 1 1 0 1 0
.oo .oo .oo&#x  | 0  1 1 |  *  *  *  * 24  * | 0 0  0  0  0 0 0  1  1  1 0 0 | 0 0 0 1 1 1 0
... ..x ...     | 0  0 2 |  *  *  *  *  * 12 | 0 0  0  0  0 0 0  0  1  0 1 1 | 0 0 0 0 1 1 1
----------------+--------+-------------------+-------------------------------+--------------
o..3x.. ...     | 3  0 0 |  3  0  0  0  0  0 | 4 *  *  *  * * *  *  *  * * * | 1 1 0 0 0 0 0
... x..3o..     | 3  0 0 |  3  0  0  0  0  0 | * 4  *  *  * * *  *  *  * * * | 1 0 1 0 0 0 0
ox. ... ...&#x  | 1  2 0 |  0  2  1  0  0  0 | * * 12  *  * * *  *  *  * * * | 0 1 0 1 0 0 0
... xo. ...&#x  | 2  1 0 |  1  2  0  0  0  0 | * *  * 12  * * *  *  *  * * * | 0 1 1 0 0 0 0
... ... ox.&#x  | 1  2 0 |  0  2  0  1  0  0 | * *  *  * 12 * *  *  *  * * * | 0 0 1 1 0 0 0
.x.3.o. ...     | 0  3 0 |  0  0  3  0  0  0 | * *  *  *  * 4 *  *  *  * * * | 0 1 0 0 1 0 0
... .o.3.x.     | 0  3 0 |  0  0  0  3  0  0 | * *  *  *  * * 4  *  *  * * * | 0 0 1 0 0 1 0
.xo ... ...&#x  | 0  2 1 |  0  0  1  0  2  0 | * *  *  *  * * * 12  *  * * * | 0 0 0 1 1 0 0
... .ox ...&#x  | 0  1 2 |  0  0  0  0  2  1 | * *  *  *  * * *  * 12  * * * | 0 0 0 0 1 1 0
... ... .xo&#x  | 0  2 1 |  0  0  0  1  2  0 | * *  *  *  * * *  *  * 12 * * | 0 0 0 1 0 1 0
..o3..x ...     | 0  0 3 |  0  0  0  0  0  3 | * *  *  *  * * *  *  *  * 4 * | 0 0 0 0 1 0 1
... ..x3..o     | 0  0 3 |  0  0  0  0  0  3 | * *  *  *  * * *  *  *  * * 4 | 0 0 0 0 0 1 1
----------------+--------+-------------------+-------------------------------+--------------
o..3x..3o..     ♦ 6  0 0 | 12  0  0  0  0  0 | 4 4  0  0  0 0 0  0  0  0 0 0 | 1 * * * * * *
ox.3xo. ...&#x  ♦ 3  3 0 |  3  6  3  0  0  0 | 1 0  3  3  0 1 0  0  0  0 0 0 | * 4 * * * * *
... xo.3ox.&#x  ♦ 3  3 0 |  3  6  0  3  0  0 | 0 1  0  3  3 0 1  0  0  0 0 0 | * * 4 * * * *
oxo ... oxo&#xt ♦ 1  4 1 |  0  4  2  2  4  0 | 0 0  2  0  2 0 0  2  0  2 0 0 | * * * 6 * * *
.xo3.ox ...&#x  ♦ 0  3 3 |  0  0  3  0  6  3 | 0 0  0  0  0 1 0  3  3  0 1 0 | * * * * 4 * *
... .ox3.xo&#x  ♦ 0  3 3 |  0  0  0  3  6  3 | 0 0  0  0  0 0 1  0  3  3 0 1 | * * * * * 4 *
..o3..x3..o     ♦ 0  0 6 |  0  0  0  0  0 12 | 0 0  0  0  0 0 0  0  0  0 4 4 | * * * * * * 1

or
o..3o..3o..     & | 12  * ♦  4  4  0  0 | 2 2  2  4  2 0 0 | 1 2 2 1
.o.3.o.3.o.       |  * 12 ♦  0  4  2  2 | 0 0  4  2  4 1 1 | 0 2 2 2
------------------+-------+-------------+------------------+--------
... x.. ...     & |  2  0 | 24  *  *  * | 1 1  0  1  0 0 0 | 1 1 1 0
oo. oo. oo.&#x  & |  1  1 |  * 48  *  * | 0 0  1  1  1 0 0 | 0 1 1 1
.x. ... ...       |  0  2 |  *  * 12  * | 0 0  2  0  0 1 0 | 0 2 0 1
... ... .x.       |  0  2 |  *  *  * 12 | 0 0  0  0  2 0 1 | 0 0 2 1
------------------+-------+-------------+------------------+--------
o..3x.. ...     & |  3  0 |  3  0  0  0 | 8 *  *  *  * * * | 1 1 0 0
... x..3o..     & |  3  0 |  3  0  0  0 | * 8  *  *  * * * | 1 0 1 0
ox. ... ...&#x  & |  1  2 |  0  2  1  0 | * * 24  *  * * * | 0 1 0 1
... xo. ...&#x  & |  2  1 |  1  2  0  0 | * *  * 24  * * * | 0 1 1 0
... ... ox.&#x  & |  1  2 |  0  2  0  1 | * *  *  * 24 * * | 0 0 1 1
.x.3.o. ...       |  0  3 |  0  0  3  0 | * *  *  *  * 4 * | 0 2 0 0
... .o.3.x.       |  0  3 |  0  0  0  3 | * *  *  *  * * 4 | 0 0 2 0
------------------+-------+-------------+------------------+--------
o..3x..3o..     & ♦  6  0 | 12  0  0  0 | 4 4  0  0  0 0 0 | 2 * * *
ox.3xo. ...&#x  & ♦  3  3 |  3  6  3  0 | 1 0  3  3  0 1 0 | * 8 * *
... xo.3ox.&#x  & ♦  3  3 |  3  6  0  3 | 0 1  0  3  3 0 1 | * * 8 *
oxo ... oxo&#xt   ♦  2  4 |  0  8  2  2 | 0 0  4  0  4 0 0 | * * * 6
```

```ooqoo3ooooo4oxoxo&#xt   → all heights = 1/2
(pt  || pseudo cube || pseudo q-oct || pseudo cube || pt)

o....3o....4o....     | 1 * * * * ♦ 8  0  0 0  0  0 0 | 12  0  0  0  0 | 6  0 0
.o...3.o...4.o...     | * 8 * * * ♦ 1  3  3 1  0  0 0 |  3  6  3  0  0 | 3  3 0
..o..3..o..4..o..     | * * 6 * * ♦ 0  0  4 0  4  0 0 |  0  4  4  4  0 | 1  4 1
...o.3...o.4...o.     | * * * 8 * ♦ 0  0  0 1  3  3 1 |  0  0  3  6  3 | 0  3 3
....o3....o4....o     | * * * * 1 ♦ 0  0  0 0  0  0 8 |  0  0  0  0 12 | 0  0 6
----------------------+-----------+-------------------+----------------+-------
oo...3oo...4oo...&#x  | 1 1 0 0 0 | 8  *  * *  *  * * |  3  0  0  0  0 | 3  0 0
..... ..... .x...     | 0 2 0 0 0 | * 12  * *  *  * * |  1  2  0  0  0 | 2  1 0
.oo..3.oo..4.oo..&#x  | 0 1 1 0 0 | *  * 24 *  *  * * |  0  2  1  0  0 | 1  2 0
.o.o.3.o.o.4.o.o.&#x  | 0 1 0 1 0 | *  *  * 8  *  * * |  0  0  3  0  0 | 0  3 0
..oo.3..oo.4..oo.&#x  | 0 0 1 1 0 | *  *  * * 24  * * |  0  0  1  2  0 | 0  2 1
..... ..... ...x.     | 0 0 0 2 0 | *  *  * *  * 12 * |  0  0  0  2  1 | 0  1 2
...oo3...oo4...oo&#x  | 0 0 0 1 1 | *  *  * *  *  * 8 |  0  0  0  0  3 | 0  0 3
----------------------+-----------+-------------------+----------------+-------
..... ..... ox...&#x  | 1 2 0 0 0 | 2  1  0 0  0  0 0 | 12  *  *  *  * | 2  0 0
..... ..... .xo..&#x  | 0 2 1 0 0 | 0  1  2 0  0  0 0 |  * 24  *  *  * | 1  1 0
.ooo.3.ooo.4.ooo.&#xt | 0 1 1 1 0 | 0  0  1 1  1  0 0 |  *  * 24  *  * | 0  2 0
..... ..... ..ox.&#x  | 0 0 1 2 0 | 0  0  0 0  2  1 0 |  *  *  * 24  * | 0  1 1
..... ..... ...xo&#x  | 0 0 0 2 1 | 0  0  0 0  0  1 2 |  *  *  *  * 12 | 0  0 2
----------------------+-----------+-------------------+----------------+-------
..... ooo..4oxo..&#xt ♦ 1 4 1 0 0 | 4  4  4 0  0  0 0 |  4  4  0  0  0 | 6  * *
.oqo. ..... .xox.&#xt ♦ 0 2 2 2 0 | 0  1  4 2  4  1 0 |  0  2  4  2  0 | * 12 *
..... ..ooo4..oxo&#xt ♦ 0 0 1 4 1 | 0  0  0 0  4  4 4 |  0  0  0  4  4 | *  * 6

or
o....3o....4o....      & | 2  * * ♦  8  0  0 0 | 12  0  0 |  6  0
.o...3.o...4.o...      & | * 16 * ♦  1  3  3 1 |  3  6  3 |  3  3
..o..3..o..4..o..        | *  * 6 ♦  0  0  8 0 |  0  8  4 |  2  4
-------------------------+--------+------------+----------+------
oo...3oo...4oo...&#x   & | 1  1 0 | 16  *  * * |  3  0  0 |  3  0
..... ..... .x...      & | 0  2 0 |  * 24  * * |  1  2  0 |  2  1
.oo..3.oo..4.oo..&#x   & | 0  1 1 |  *  * 48 * |  0  2  1 |  1  2
.o.o.3.o.o.4.o.o.&#x     | 0  2 0 |  *  *  * 8 |  0  0  3 |  0  3
-------------------------+--------+------------+----------+------
..... ..... ox...&#x   & | 1  2 0 |  2  1  0 0 | 24  *  * |  2  0
..... ..... .xo..&#x   & | 0  2 1 |  0  1  2 0 |  * 48  * |  1  1
.ooo.3.ooo.4.ooo.&#xt    | 0  2 1 |  0  0  2 1 |  *  * 24 |  0  2
-------------------------+--------+------------+----------+------
..... ooo..4oxo..&#xt  & ♦ 1  4 1 |  4  4  4 0 |  4  4  0 | 12  *
.oqo. ..... .xox.&#xt    ♦ 0  4 2 |  0  2  8 2 |  0  4  4 |  * 12
```