Acronym bicyte ausodip Name bicyclotetraugmented square-octagon duoprism Circumradius ... Lace cityin approx. ASCII-art ```x4o x4x x4o - squobcu x4x w4o x4x - pactic x4o x4x x4o - squobcu ``` ```o4o o4x o4x o4o - esquidpy o4x q4o q4o o4x - pexco o4x q4o q4o o4x - pexco o4o o4x o4x o4o - esquidpy ``` Dihedral angles at {3} between oct and trip:   150° at {4} between squobcu and trip:   arccos(-1/sqrt(3)) = 125.264390° at {3} between esquidpy and oct:   120° at {3} between oct and oct:   120° at {3} between oct and squobcu:   120° at {4} between esquidpy and squobcu:   90° at {4} between squobcu and squobcu:   90° Pattern(parts of total size:4x8 squares) ```A---1---A---2---A---1---A---2---A-... | \ / | | \ / | | 3==B,C==3===4===3==B,C==3===4===3= | / \ | | / \ | | A---1---A---2---A---1---A---2---A-... | \ / | | \ / | | 3==B,C==3===4===3==B,C==3===4===3= | / \ | | / \ | | A---1---A---2---A---1---A---2---A-... | \ / | | \ / | | 3==B,C==3===4===3==B,C==3===4===3= | / \ | | / \ | | A---1---A---2---A---1---A---2---A-... | \ / | | \ / | | 3==B,C==3===4===3==B,C==3===4===3= | / \ | | / \ | | (A)-1--(A)--2--(A)--1--(A)--2--(A)-.. (in each column the B's are to be identified) ``` Confer uniform relative: ico   srit   sodip   segmentochora: ticcup   {4} || op   cubpy   related CRFs: pexic   pacsrit   cyte cubau sodip   cyte opau sodip   general polytopal classes: partial Stott expansions   bistratic lace towers

This CRF polychoron can be obtained by augmenting alternate cubes of sodip with cubpy and all ops by {4} || op. Note, that the squippies then either reconnect to octs or blend with the remaining cubes into esquidpies. Moreover the squacues combine by pairs into squobcues.

It likewise can be obtained from srit by splitting into 3 segments, rejecting the central ticcup, recombining the outer parts, and then apply the same operation to that bicupola in an orthogonal direction – thus resulting in a partial Stott contraction (cf. esp. the lace city display of srit).

Conversely it can be obtained by 2 orthogonally applied axial partial Stott expansions based on ico.

Incidence matrix according to Dynkin symbol

```oxo4xxw oxo4qoo&#zx   → all heights = 0
(tegum sum of (q,q,x,x)-tes, sodip, and a w-{4})

o..4o.. o..4o..     | 16  * * |  2  4  0  0  0  0 | 1  2  4  2  0  0  0 | 2  2  1 0 (C)
.o.4.o. .o.4.o.     |  * 32 * |  0  2  1  1  2  1 | 0  2  2  2  2  1  2 | 1  2  2 1 (A)
..o4..o ..o4..o     |  *  * 4 ♦  0  0  0  0  0  8 | 0  0  0  0  0  4  8 | 0  0  4 2 (B)
--------------------+---------+-------------------+---------------------+----------
... x.. ... ...     |  2  0 0 | 16  *  *  *  *  * | 1  0  2  0  0  0  0 | 2  1  0 0 (4)
oo.4oo. oo.4oo.&#x  |  1  1 0 |  * 64  *  *  *  * | 0  1  1  1  0  0  0 | 1  1  1 0
.x. ... ... ...     |  0  2 0 |  *  * 16  *  *  * | 0  2  0  0  0  1  0 | 1  0  2 0 (1)
... .x. ... ...     |  0  2 0 |  *  *  * 16  *  * | 0  0  2  0  2  0  0 | 1  2  0 1 (2)
... ... .x. ...     |  0  2 0 |  *  *  *  * 32  * | 0  0  0  1  1  0  1 | 0  1  1 1 (3)
.oo4.oo .oo4.oo&#x  |  0  1 1 |  *  *  *  *  * 32 | 0  0  0  0  0  1  2 | 0  0  2 1
--------------------+---------+-------------------+---------------------+----------
o..4x.. ... ...     |  4  0 0 |  4  0  0  0  0  0 | 4  *  *  *  *  *  * | 2  0  0 0
ox. ... ... ...&#x  |  1  2 0 |  0  2  1  0  0  0 | * 32  *  *  *  *  * | 1  0  1 0
... xx. ... ...&#x  |  2  2 0 |  1  2  0  1  0  0 | *  * 32  *  *  *  * | 1  1  0 0
... ... ox. ...&#x  |  1  2 0 |  0  2  0  0  1  0 | *  *  * 32  *  *  * | 0  1  1 0
... .x. .x. ...     |  0  4 0 |  0  0  0  2  2  0 | *  *  *  * 16  *  * | 0  1  0 1
.xo ... ... ...&#x  |  0  2 1 |  0  0  1  0  0  2 | *  *  *  *  * 16  * | 0  0  2 0
... ... .xo ...&#x  |  0  2 1 |  0  0  0  0  1  2 | *  *  *  *  *  * 32 | 0  0  1 1
--------------------+---------+-------------------+---------------------+----------
ox.4xx. ... qo.&#zx ♦  8  8 0 |  8 16  4  4  0  0 | 2  8  8  0  0  0  0 | 4  *  * *
... xx. ox. ...&#x  ♦  2  4 0 |  1  4  0  2  2  0 | 0  0  2  2  1  0  0 | * 16  * *
oxo ... oxo ...&#xt ♦  1  4 1 |  0  4  2  0  2  4 | 0  2  0  2  0  2  2 | *  * 16 *
... .xw .xo4.oo&#zx ♦  0  8 2 |  0  0  0  4  8  8 | 0  0  0  0  4  0  8 | *  *  * 4
```

```(qo)(qo)(qo) (ox)(xo)(ox)4(xx)(xw)(xx)&#xt   → both heights = 1/sqrt(2) = 0.707107
(squobcu || pseudo pactic || squobcu)

(o.)(..)(..) (o.)(..)(..)4(o.)(..)(..)     & | 16  *  * * |  2  2  2 0 0  0  0 0 0  0 | 1  1  2  1  2  2  0 0  0 0 | 1 1  1  2 0
(.o)(..)(..) (.o)(..)(..)4(.o)(..)(..)     & |  * 16  * * |  0  2  0 1 1  2  1 0 0  0 | 0  2  2  0  0  2  2 1  2 0 | 1 0  2  2 1
(..)(o.)(..) (..)(o.)(..)4(..)(o.)(..)       |  *  * 16 * |  0  0  2 0 0  2  0 1 1  1 | 0  0  0  2  2  2  2 0  2 1 | 0 1  2  2 1
(..)(.o)(..) (..)(.o)(..)4(..)(.o)(..)       |  *  *  * 4 ♦  0  0  0 0 0  0  4 0 0  4 | 0  0  0  0  0  0  0 2  8 2 | 0 0  4  0 2
---------------------------------------------+------------+---------------------------+----------------------------+------------
(..)(..)(..) (..)(..)(..) (x.)(..)(..)     & |  2  0  0 0 | 16  *  * * *  *  * * *  * | 1  0  1  0  1  0  0 0  0 0 | 1 1  0  1 0
(oo)(..)(..) (oo)(..)(..)4(oo)(..)(..)&#x  & |  1  1  0 0 |  * 32  * * *  *  * * *  * | 0  1  1  0  0  1  0 0  0 0 | 1 0  1  1 0
(o.)(o.)(..) (o.)(o.)(..)4(o.)(o.)(..)&#x  & |  1  0  1 0 |  *  * 32 * *  *  * * *  * | 0  0  0  1  1  1  0 0  0 0 | 0 1  1  1 0
(..)(..)(..) (.x)(..)(..) (..)(..)(..)     & |  0  2  0 0 |  *  *  * 8 *  *  * * *  * | 0  2  0  0  0  0  0 1  0 0 | 1 0  2  0 0
(..)(..)(..) (..)(..)(..) (.x)(..)(..)     & |  0  2  0 0 |  *  *  * * 8  *  * * *  * | 0  0  2  0  0  0  2 0  0 0 | 1 0  0  2 1
(.o)(o.)(..) (.o)(o.)(..)4(.o)(o.)(..)&#x  & |  0  1  1 0 |  *  *  * * * 32  * * *  * | 0  0  0  0  0  1  1 0  1 0 | 0 0  1  1 1
(.o)(.o)(..) (.o)(.o)(..)4(.o)(.o)(..)&#x  & |  0  1  0 1 |  *  *  * * *  * 16 * *  * | 0  0  0  0  0  0  0 1  2 0 | 0 0  2  0 1
(..)(..)(..) (..)(x.)(..) (..)(..)(..)       |  0  0  2 0 |  *  *  * * *  *  * 8 *  * | 0  0  0  2  0  0  0 0  0 1 | 0 1  2  0 0
(..)(..)(..) (..)(..)(..) (..)(x.)(..)       |  0  0  2 0 |  *  *  * * *  *  * * 8  * | 0  0  0  0  2  0  2 0  0 0 | 0 1  0  2 1
(..)(oo)(..) (..)(oo)(..)4(..)(oo)(..)&#x    |  0  0  1 1 |  *  *  * * *  *  * * * 16 | 0  0  0  0  0  0  0 0  2 1 | 0 0  2  0 1
---------------------------------------------+------------+---------------------------+----------------------------+------------
(..)(..)(..) (o.)(..)(..) (x.)(..)(..)     & |  4  0  0 0 |  4  0  0 0 0  0  0 0 0  0 | 4  *  *  *  *  *  * *  * * | 1 1  0  0 0
(..)(..)(..) (ox)(..)(..) (..)(..)(..)&#x  & |  1  2  0 0 |  0  2  0 1 0  0  0 0 0  0 | * 16  *  *  *  *  * *  * * | 1 0  1  0 0
(..)(..)(..) (..)(..)(..) (xx)(..)(..)&#x  & |  2  2  0 0 |  1  2  0 0 1  0  0 0 0  0 | *  * 16  *  *  *  * *  * * | 1 0  0  1 0
(..)(..)(..) (o.)(x.)(..) (..)(..)(..)&#x  & |  1  0  2 0 |  0  0  2 0 0  0  0 1 0  0 | *  *  * 16  *  *  * *  * * | 0 1  1  0 0
(..)(..)(..) (..)(..)(..) (x.)(x.)(..)&#x  & |  2  0  2 0 |  1  0  2 0 0  0  0 0 1  0 | *  *  *  * 16  *  * *  * * | 0 1  0  1 0
(oo)(o.)(..) (oo)(o.)(..)4(oo)(o.)(..)&#x  & |  1  1  1 0 |  0  1  1 0 0  1  0 0 0  0 | *  *  *  *  * 32  * *  * * | 0 0  1  1 0
(..)(..)(..) (..)(..)(..) (.x)(x.)(..)&#x  & |  0  2  2 0 |  0  0  0 0 1  2  0 0 1  0 | *  *  *  *  *  * 16 *  * * | 0 0  0  1 1
(..)(..)(..) (.x)(.o)(..) (..)(..)(..)&#x  & |  0  2  0 1 |  0  0  0 1 0  0  2 0 0  0 | *  *  *  *  *  *  * 8  * * | 0 0  2  0 0
(.o)(oo)(..) (.o)(oo)(..)4(.o)(oo)(..)&#x  & |  0  1  1 1 |  0  0  0 0 0  1  1 0 0  1 | *  *  *  *  *  *  * * 32 * | 0 0  1  0 1
(..)(..)(..) (..)(xo)(..) (..)(..)(..)&#x    |  0  0  2 1 |  0  0  0 0 0  0  0 1 0  2 | *  *  *  *  *  *  * *  * 8 | 0 0  2  0 0
---------------------------------------------+------------+---------------------------+----------------------------+------------
(qo)(..)(..) (ox)(..)(..)4(xx)(..)(..)&#zx & ♦  8  8  0 0 |  8 16  0 4 4  0  0 0 0  0 | 2  8  8  0  0  0  0 0  0 0 | 2 *  *  * *
(..)(..)(..) (o.)(x.)(o.)4(x.)(x.)(x.)&#xt   ♦  8  0  8 0 |  8  0 16 0 0  0  0 4 4  0 | 2  0  0  8  8  0  0 0  0 0 | * 2  *  * *
(..)(..)(..) (ox)(xo)(..) (..)(..)(..)&#x  & ♦  1  2  2 1 |  0  2  2 1 0  2  2 1 0  2 | 0  1  0  1  0  2  0 1  2 1 | * * 16  * *
(..)(..)(..) (..)(..)(..) (xx)(x.)(..)&#x  & ♦  2  2  2 0 |  1  2  2 0 1  2  0 0 1  0 | 0  0  1  0  1  2  1 0  0 0 | * *  * 16 *
(.o)(qo)(.o) (..)(..)(..) (.x)(xw)(.x)&#xt   ♦  0  4  4 2 |  0  0  0 0 2  8  4 0 2  4 | 0  0  0  0  0  0  4 0  8 0 | * *  *  * 4
```