Acronym ... TOCID symbol OC* Name oct+6{4} (?) Circumradius 1/sqrt(2) = 0.707107 Vertex figure [(3/2,4)4] = [(3,4)4]/3 Snub derivation Coordinates (1/sqrt(2), 0, 0)   & all permutations, all changes of sign General of army oct Colonel of regiment oct Confer 2oct+6{4}   2oct+12{4}

Looks like a compound of an octahedra (oct) plus 3 diametral pairs of squares, and indeed edges and {4} coincide by pairs, but vertices are identified (type A). Alternatively it can be seen as a pair of tetrahemihexahedra (thah), mutually in inverted positioning, with vertices pairwise identified.

Incidence matrix according to Dynkin symbol

```x3/2o4o4*a (type A)

.   . .    | 6 |  8 | 4 4
-----------+---+----+----
x   . .    | 2 | 24 | 1 1
-----------+---+----+----
x3/2o .    | 3 |  3 | 8 *
x   . o4*a | 4 |  4 | * 6
```

```o4/3x3o4*a (type A)

.   . . | 6 |  8 | 4 4
--------+---+----+----
.   x . | 2 | 24 | 1 1
--------+---+----+----
o4/3x . | 4 |  4 | 6 *
.   x3o | 3 |  3 | * 8
```

```o4/3o3x4*a (type A)

.   . .    | 6 |  8 | 4 4
-----------+---+----+----
.   . x    | 2 | 24 | 1 1
-----------+---+----+----
.   o3x    | 3 |  3 | 8 *
o   . x4*a | 4 |  4 | * 6
```

```x4/3o4/3o3/2*a (type A)

.   .   .      | 6 |  8 | 4 4
---------------+---+----+----
x   .   .      | 2 | 24 | 1 1
---------------+---+----+----
x4/3o   .      | 4 |  4 | 6 *
x   .   o3/2*a | 3 |  3 | * 8
```

```β3o4o (type A)

both( . . . ) | 6 |  8 | 4 4
--------------+---+----+----
sefa( β3o . ) | 2 | 24 | 1 1
--------------+---+----+----
β3o .   ♦ 3 |  3 | 8 *
sefa( β3o4o ) | 4 |  4 | * 6

starting figure: x3o4o
```

```β3/2o4o (type A)

both( .   . . ) | 6 |  8 | 4 4
----------------+---+----+----
sefa( β3/2o . ) | 2 | 24 | 1 1
----------------+---+----+----
β3/2o .   ♦ 3 |  3 | 8 *
sefa( β3/2o4o ) | 4 |  4 | * 6

starting figure: x3/2o4o
```

```o4/3o3β (type A)

both( .   . . ) | 6 |  8 | 4 4
----------------+---+----+----
sefa( .   o3β ) | 2 | 24 | 1 1
----------------+---+----+----
.   o3β   ♦ 3 |  3 | 8 *
sefa( o4/3o3β ) | 4 |  4 | * 6

starting figure: o4/3o3x
```

```o4/3o3/2β (type A)

both( .   .   . ) | 6 |  8 | 4 4
------------------+---+----+----
sefa( .   o3/2β ) | 2 | 24 | 1 1
------------------+---+----+----
.   o3/2β   ♦ 3 |  3 | 8 *
sefa( o4/3o3/2β ) | 4 |  4 | * 6

starting figure: o4/3o3/2x
```

```o3β3o (type A)

both( . . . ) | 6 |  4  4 | 2 2 4
--------------+---+-------+------
sefa( o3β . ) | 2 | 12  * | 1 0 1
sefa( . β3o ) | 2 |  * 12 | 0 1 1
--------------+---+-------+------
o3β .   ♦ 3 |  3  0 | 4 * *
. β3o   ♦ 3 |  0  3 | * 4 *
sefa( o3β3o ) | 4 |  2  2 | * * 6

starting figure: o3x3o
```

```o3/2β3o (type A)

both( .   . . ) | 6 |  4  4 | 2 2 4
----------------+---+-------+------
sefa( o3/2β . ) | 2 | 12  * | 1 0 1
sefa( .   β3o ) | 2 |  * 12 | 0 1 1
----------------+---+-------+------
o3/2β .   ♦ 3 |  3  0 | 4 * *
.   β3o   ♦ 3 |  0  3 | * 4 *
sefa( o3/2β3o ) | 4 |  2  2 | * * 6

starting figure: o3/2x3o
```

```o3/2β3/2o (type A)

both( .   .   . ) | 6 |  4  4 | 2 2 4
------------------+---+-------+------
sefa( o3/2β   . ) | 2 | 12  * | 1 0 1
sefa( .   β3/2o ) | 2 |  * 12 | 0 1 1
------------------+---+-------+------
o3/2β   .   ♦ 3 |  3  0 | 4 * *
.   β3/2o   ♦ 3 |  0  3 | * 4 *
sefa( o3/2β3/2o ) | 4 |  2  2 | * * 6

starting figure: o3/2x3/2o
```