©

a---b---a---b---a---b---a---b---
|   |   |   |   |   |   |   |
c---d---c---d---c---d---c---d---
|   |   |   |   |   |   |   |
a---b---a---b---a---b---a---b---
|   |   |   |   |   |   |   |
c---d---c---d---c---d---c---d---
|   |   |   |   |   |   |   |
a---b---a---b---a---b---a---b---
|   |   |   |   |   |   |   |
c---d---c---d---c---d---c---d---
|   |   |   |   |   |   |   |
a---b---a---b---a---b---a---b---
|   |   |   |   |   |   |   |
c---d---c---d---c---d---c---d---
|   |   |   |   |   |   |   |

Comes in 2 types, depending on the pairs of coplanar squares (in dual positioning): being counted separately (type A) or being combined to compounds (socs) as well (type B).

Incidence matrix according to Dynkin symbol

(Type A: no identifications)

64 |   4 |  4  2 |  4 || 1
---+-----+-------+----++--
 2 | 128 |  2  1 |  3 || 1
---+-----+-------+----++--
 4 |   4 | 64  * |  2 || 1  within pattern plane
 4 |   4 |  * 32 |  2 || 1  orthogonal to pattern plane
---+-----+-------+----++--
 8 |  12 |  4  2 | 32 || 1  cube
---+-----+-------+----++--
16 |  32 | 16  8 |  8 || 4  tes

(Type B: compounded squares)

64 |   4 |  4  2 |  4 || 1
---+-----+-------+----++--
 2 | 128 |  2  1 |  3 || 1
---+-----+-------+----++--
 4 |   4 | 64  * |  2 || 1
 8 |   8 |  * 16 |  2 || 2  soc (2{4}-comp.)
---+-----+-------+----++--
16 |  24 |  8  2 | 16 || 2  (2{4}-comp.)-prism
---+-----+-------+----++--
16 |  32 | 16  8 |  8 || 4  tes