Acronym bicyte ausodip
Name bicyclotetraugmented square-octagon duoprism
Circumradius ...
Lace city
in 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
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

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