Acronym poxic   (alt.: phic srico, alt.: owau sidpith)
Name partially octa-expanded icositetrachoron,
partially hexadeca-contracted small rhombated icositetrachoron,
octa-augmented small diprismated tesseractithexadecachoron
  ©  
Circumradius ...
Lace city
in approx. ASCII-art
              o4o              
                               
          x4o     x4o          
                               
                               
    x4o   x4x     x4x   x4o    
                               
o4o           o4w           o4o
                               
    x4o   x4x     x4x   x4o    
                               
                               
          x4o     x4o          
                               
              o4o              
Coordinates
  1. ((1+sqrt(2))/2, 1/2, 1/2, 1/2)   & all permutations, all changes of sign
    (vertex inscribed sidpith)
  2. ((2+sqrt(2))/2, 0, 0, 0)            & all permutations, all changes of sign
    (vertex inscribed w-hex)
Dihedral angles
Confer
uniform relative:
ico   srico   sidpith  
related segmentochora:
cubpy   cubasirco  
related CRFs:
oox3ooo4oxx&#xt   pocsric   oxwQ wxoo3xxxx4oxxo&#zx   dapabdi poxic  
general polytopal classes:
partial Stott expansions  
External
links
quickfur  

This CRF polychoron can be obtained from ico by partial Stott expanding only 8 of its vertices (in hexadecachoral positioning). – Note that its octs thereby become elongated into esquidpies, by themselves thus outlining a somehow thickened edge skeleton of hex. And, in this comparison to hex, the other cells too can be understood either as its former cells (tets) resp. as its likewise thickened former triangular faces (trips).

Conversely it can be obtained by a similar partial Stott contraction from pocsric (which in turn is derived by such a contraction from srico).

Alternatively it can be obtained by augmenting the 8 full symmetrical cubes of sidpith by cubpy. Then the thus introduced squippies would recombine with the remaining (only prism symmetric) cubes into esquidpies.


Incidence matrix according to Dynkin symbol

wx3oo3oo4ox&#zx   → height = 0
(tegum sum of w-hex and sidpith)

o.3o.3o.4o.     | 8  *   8  0  0 | 12  0  0 |  6  0  0
.o3.o3.o4.o     | * 64 |  1  3  3 |  3  3  6 |  3  1  3
----------------+------+----------+----------+---------
oo3oo3oo4oo&#x  | 1  1 | 64  *  * |  3  0  0 |  3  0  0
.x .. .. ..     | 0  2 |  * 96  * |  0  2  2 |  1  1  2
.. .. .. .x     | 0  2 |  *  * 96 |  1  0  2 |  2  0  1
----------------+------+----------+----------+---------
.. .. .. ox&#x  | 1  2 |  2  0  1 | 96  *  * |  2  0  0
.x3.o .. ..     | 0  3 |  0  3  0 |  * 64  * |  0  1  1
.x .. .. .x     | 0  4 |  0  2  2 |  *  * 96 |  1  0  1
----------------+------+----------+----------+---------
wx .. oo4ox&#zx  2  8 |  8  4  8 |  8  0  4 | 24  *  *
.x3.o3.o ..      0  4 |  0  6  0 |  0  4  0 |  * 16  *
.x3.o .. .x      0  6 |  0  6  3 |  0  2  3 |  *  * 32

wxx3ooo3oqo *b3ooq&#zx   → height = 0
(tegum sum of w-hex and 2 mutually gyrated (x,q)-rits)

o..3o..3o.. *b3o..     | 8  *  *   4  4  0  0  0 | 12  0  0  0 |  6 0  0 0
.o.3.o.3.o. *b3.o.     | * 32  * |  1  0  3  3  0 |  3  3  6  0 |  3 1  3 0
..o3..o3..o *b3..o     | *  * 32 |  0  1  0  3  3 |  3  0  6  3 |  3 0  3 1
-----------------------+---------+----------------+-------------+----------
oo.3oo.3oo. *b3oo.&#x  | 1  1  0 | 32  *  *  *  * |  3  0  0  0 |  3 0  0 0
o.o3o.o3o.o *b3o.o&#x  | 1  0  1 |  * 32  *  *  * |  3  0  0  0 |  3 0  0 0
.x. ... ...    ...     | 0  2  0 |  *  * 48  *  * |  0  2  2  0 |  1 1  2 0
.oo3.oo3.oo *b3.oo&#x  | 0  1  1 |  *  *  * 96  * |  1  0  2  0 |  2 0  1 0
..x ... ...    ...     | 0  0  2 |  *  *  *  * 48 |  0  0  2  2 |  1 0  2 1
-----------------------+---------+----------------+-------------+----------
ooo3ooo3ooo *b3ooo&#x  | 1  1  1 |  1  1  0  1  0 | 96  *  *  * |  2 0  0 0
.x.3.o. ...    ...     | 0  3  0 |  0  0  3  0  0 |  * 32  *  * |  0 1  1 0
.xx ... ...    ...&#x  | 0  2  2 |  0  0  1  2  1 |  *  * 96  * |  1 0  1 0
..x3..o ...    ...     | 0  0  3 |  0  0  0  0  3 |  *  *  * 32 |  0 0  1 1
-----------------------+---------+----------------+-------------+----------
wxx ... oqo    ooq&#zx  2  4  4 |  4  4  2  8  2 |  8  0  4  0 | 24 *  * *
.x.3.o. ... *b3.o.      0  4  0 |  0  0  6  0  0 |  0  4  0  0 |  * 8  * *
.xx3.oo ...    ...&#x   0  3  3 |  0  0  3  3  3 |  0  1  3  1 |  * * 32 *
..x3..o3..o    ...      0  0  4 |  0  0  0  0  6 |  0  0  0  4 |  * *  * 8

oxwU wxoo3oooo4oxxo&#zx   → height = 0  (U=w+x=q+u=q+2x)
(tegum sum of equatorial w-oct, sircope, (w,x)-tes, and ortho U-line)

o... o...3o...4o...     | 6  *  * *   8  0  0  0  0  0  0 |  4  8  0  0  0  0  0  0 |  4  2 0  0  0
.o.. .o..3.o..4.o..     | * 48  * * |  1  1  2  2  1  0  0 |  1  2  2  1  2  2  2  0 |  2  1 1  1  2
..o. ..o.3..o.4..o.     | *  * 16 * |  0  0  0  0  3  3  1 |  0  0  0  0  0  3  6  3 |  0  3 0  1  3
...o ...o3...o4...o     | *  *  * 2   0  0  0  0  0  0  8 |  0  0  0  0  0  0  0 12 |  0  6 0  0  0
------------------------+-----------+----------------------+-------------------------+--------------
oo.. oo..3oo..4oo..&#x  | 1  1  0 0 | 48  *  *  *  *  *  * |  1  2  0  0  0  0  0  0 |  2  1 0  0  0
.x.. .... .... ....     | 0  2  0 0 |  * 24  *  *  *  *  * |  1  0  2  0  0  0  0  0 |  2  0 1  0  0
.... .x.. .... ....     | 0  2  0 0 |  *  * 48  *  *  *  * |  0  0  1  1  1  1  0  0 |  1  0 1  1  1
.... .... .... .x..     | 0  2  0 0 |  *  *  * 48  *  *  * |  0  1  0  0  1  0  1  0 |  1  1 0  0  1
.oo. .oo.3.oo.4.oo.&#x  | 0  1  1 0 |  *  *  *  * 48  *  * |  0  0  0  0  0  2  2  0 |  0  1 0  1  2
.... .... .... ..x.     | 0  0  2 0 |  *  *  *  *  * 24  * |  0  0  0  0  0  0  2  1 |  0  2 0  0  1
..oo ..oo3..oo4..oo&#x  | 0  0  1 1 |  *  *  *  *  *  * 16 |  0  0  0  0  0  0  0  3 |  0  3 0  0  0
------------------------+-----------+----------------------+-------------------------+--------------
ox.. .... .... ....&#x  | 1  2  0 0 |  2  1  0  0  0  0  0 | 24  *  *  *  *  *  *  * |  2  0 0  0  0
.... .... .... ox..&#x  | 1  2  0 0 |  2  0  0  1  0  0  0 |  * 48  *  *  *  *  *  * |  1  1 0  0  0
.x.. .x.. .... ....     | 0  4  0 0 |  0  2  2  0  0  0  0 |  *  * 24  *  *  *  *  * |  1  0 1  0  0
.... .x..3.o.. ....     | 0  3  0 0 |  0  0  3  0  0  0  0 |  *  *  * 16  *  *  *  * |  0  0 1  1  0
.... .x.. .... .x..     | 0  4  0 0 |  0  0  2  2  0  0  0 |  *  *  *  * 24  *  *  * |  1  0 0  0  1
.... .xo. .... ....&#x  | 0  2  1 0 |  0  0  1  0  2  0  0 |  *  *  *  *  * 48  *  * |  0  0 0  1  1
.... .... .... .xx.&#x  | 0  2  2 0 |  0  0  0  1  2  1  0 |  *  *  *  *  *  * 48  * |  0  1 0  0  1
.... .... .... ..xo&#x  | 0  0  2 1 |  0  0  0  0  0  1  2 |  *  *  *  *  *  *  * 24 |  0  2 0  0  0
------------------------+-----------+----------------------+-------------------------+--------------
ox.. wx.. .... ox..&#zx  2  8  0 0 |  8  4  4  4  0  0  0 |  4  4  2  0  2  0  0  0 | 12  * *  *  *
.... .... oooo4oxxo&#xt  1  4  4 1 |  4  0  0  4  4  4  4 |  0  4  0  0  0  0  4  4 |  * 12 *  *  *
.x.. .x..3.o.. ....      0  6  0 0 |  0  3  6  0  0  0  0 |  0  0  3  2  0  0  0  0 |  *  * 8  *  *
.... .xo.3.oo. ....&#x   0  3  1 0 |  0  0  3  0  3  0  0 |  0  0  0  1  0  3  0  0 |  *  * * 16  *
.... .xo. .... .xx.&#x   0  4  2 0 |  0  0  2  2  4  1  0 |  0  0  0  0  1  2  2  0 |  *  * *  * 24

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