Acronym pexic
Name partially (mono-)expanded icositetrachoron
Circumradius ...
Lace city
in approx. ASCII-art
   o3x   x3o   
               
x3o   x3x   o3x
               
               
x3o   x3x   o3x
               
   o3x   x3o   
o4o  x4o  o4o		- oct
             
x4o  o4q  x4o		- co
             
             
x4o  o4q  x4o		- co
             
o4o  x4o  o4o		- oct

 |    |    +-- esquidpy
 |    +------- pexco
 +------------ esquidpy
Dihedral angles
  • at {3} between oct and trip:   150°
  • at {4} between esquidpy and trip:   arccos(-1/sqrt(3)) = 125.264390°
  • at {3} between esquidpy and oct:   120°
  • at {3} between oct and oct:   120°
Confer
uniform relative:
ico   srit  
segmentochora:
cope   oct || co   oct || tricu   {6} || oct  
related CRFs:
bicyte ausodip   pacsrit   eoctaco  
general polytopal classes:
partial Stott expansions   bistratic lace towers  

Incidence matrix according to Dynkin symbol

xoox3oxxo4oooo&#xt   → outer heights = 1/sqrt(2) = 0.707107
                       inner height = 1
(oct || pseudo co || pseudo co || oct)

o...3o...4o...      & | 12  *   4  4  0  0 |  4  4  4  0  0 | 1  4 1 0
.o..3.o..4.o..      & |  * 24 |  0  2  4  1 |  0  1  4  2  4 | 0  2 2 2
----------------------+-------+-------------+----------------+---------
x... .... ....      & |  2  0 | 24  *  *  * |  2  1  0  0  0 | 1  2 0 0
oo..3oo..4oo..&#x   & |  1  1 |  * 48  *  * |  0  1  2  0  0 | 0  2 1 0
.... .x.. ....      & |  0  2 |  *  * 48  * |  0  0  1  1  1 | 0  1 1 1
.oo.3.oo.4.oo.&#x     |  0  2 |  *  *  * 12 |  0  0  0  0  4 | 0  0 2 2
----------------------+-------+-------------+----------------+---------
x...3o... ....      & |  3  0 |  3  0  0  0 | 16  *  *  *  * | 1  1 0 0
xo.. .... ....&#x   & |  2  1 |  1  2  0  0 |  * 24  *  *  * | 0  2 0 0
.... ox.. ....&#x   & |  1  2 |  0  2  1  0 |  *  * 48  *  * | 0  1 1 0
.o..3.x.. ....      & |  0  3 |  0  0  3  0 |  *  *  * 16  * | 0  1 0 1
.... .xx. ....&#x     |  0  4 |  0  0  2  2 |  *  *  *  * 24 | 0  0 1 1
----------------------+-------+-------------+----------------+---------
x...3o...4o...      &   6  0 | 12  0  0  0 |  8  0  0  0  0 | 2  * * *
xo..3ox.. ....&#x   &   3  3 |  3  6  3  0 |  1  3  3  1  0 | * 16 * *
.... oxxo4oooo&#xt      2  8 |  0  8  8  4 |  0  0  8  0  4 | *  * 6 *
.oo.3.xx. ....&#x       0  6 |  0  0  6  3 |  0  0  0  2  3 | *  * * 8

oxxo3xoox3oxxo&#xt   → outer heights = 1/sqrt(2) = 0.707107
                       inner height = 1
(oct || pseudo co || pseudo co || oct)

o...3o...3o...     & | 12  *   4  4  0  0  0 | 2 2  2  4  2 0 0  0  0 | 1 2 2 1 0 0
.o..3.o..3.o..     & |  * 24 |  0  2  2  2  1 | 0 0  2  1  2 1 1  2  2 | 0 1 1 2 1 1
---------------------+-------+----------------+------------------------+------------
.... x... ....     & |  2  0 | 24  *  *  *  * | 1 1  0  1  0 0 0  0  0 | 1 1 1 0 0 0
oo..3oo..3oo..&#x  & |  1  1 |  * 48  *  *  * | 0 0  1  1  1 0 0  0  0 | 0 1 1 1 0 0
.x.. .... ....     & |  0  2 |  *  * 24  *  * | 0 0  1  0  0 1 0  1  0 | 0 1 0 1 1 0
.... .... .x..     & |  0  2 |  *  *  * 24  * | 0 0  0  0  1 0 1  0  1 | 0 0 1 1 0 1
.oo.3.oo.3.oo.&#x    |  0  2 |  *  *  *  * 12 | 0 0  0  0  0 0 0  2  2 | 0 0 0 2 1 1
---------------------+-------+----------------+------------------------+------------
o...3x... ....     & |  3  0 |  3  0  0  0  0 | 8 *  *  *  * * *  *  * | 1 1 0 0 0 0
.... x...3o...     & |  3  0 |  3  0  0  0  0 | * 8  *  *  * * *  *  * | 1 0 1 0 0 0
ox.. .... ....&#x  & |  1  2 |  0  2  1  0  0 | * * 24  *  * * *  *  * | 0 1 0 1 0 0
.... xo.. ....&#x  & |  2  1 |  1  2  0  0  0 | * *  * 24  * * *  *  * | 0 1 1 0 0 0
.... .... ox..&#x  & |  1  2 |  0  2  0  1  0 | * *  *  * 24 * *  *  * | 0 0 1 1 0 0
.x..3.o.. ....     & |  0  3 |  0  0  3  0  0 | * *  *  *  * 8 *  *  * | 0 1 0 0 1 0
.... .o..3.x..     & |  0  3 |  0  0  0  3  0 | * *  *  *  * * 8  *  * | 0 0 1 0 0 1
.xx. .... ....&#x    |  0  4 |  0  0  2  0  2 | * *  *  *  * * * 12  * | 0 0 0 1 1 0
.... .... .xx.&#x    |  0  4 |  0  0  0  2  2 | * *  *  *  * * *  * 12 | 0 0 0 1 0 1
---------------------+-------+----------------+------------------------+------------
o...3x...3o...     &   6  0 | 12  0  0  0  0 | 4 4  0  0  0 0 0  0  0 | 2 * * * * *
ox..3xo.. ....&#x  &   3  3 |  3  6  3  0  0 | 1 0  3  3  0 1 0  0  0 | * 8 * * * *
.... xo..3ox..&#x  &   3  3 |  3  6  0  3  0 | 0 1  0  3  3 0 1  0  0 | * * 8 * * *
oxxo .... oxxo&#xt     2  8 |  0  8  4  4  4 | 0 0  4  0  4 0 0  2  2 | * * * 6 * *
.xx.3.oo. ....&#x      0  6 |  0  0  6  0  3 | 0 0  0  0  0 2 0  3  0 | * * * * 4 *
.... .oo.3.xx.&#x      0  6 |  0  0  0  6  3 | 0 0  0  0  0 0 2  0  3 | * * * * * 4

wx xo3ox4oo&#zx   → height = 0
(tegum sum of (w,x)-ope and cope)

o. o.3o.4o.     | 12  *   4  4  0  0 |  4  4  4  0  0 | 1 1  4 0
.o .o3.o4.o     |  * 24 |  0  2  1  4 |  0  1  4  4  2 | 0 2  2 2
----------------+-------+-------------+----------------+---------
.. x. .. ..     |  2  0 | 24  *  *  * |  2  1  0  0  0 | 1 0  2 0
oo oo3oo4oo&#x  |  1  1 |  * 48  *  * |  0  1  2  0  0 | 0 1  2 0
.x .. .. ..&#x  |  0  2 |  *  * 12  * |  0  0  0  4  0 | 0 2  0 2
.. .. .x ..     |  0  2 |  *  *  * 48 |  0  0  1  1  1 | 0 1  1 1
----------------+-------+-------------+----------------+---------
.. x.3o. ..     |  3  0 |  3  0  0  0 | 16  *  *  *  * | 1 0  1 0
.. xo .. ..&#x  |  2  1 |  1  2  0  0 |  * 24  *  *  * | 0 0  2 0
.. .. ox ..&#x  |  1  2 |  0  2  0  1 |  *  * 48  *  * | 0 1  1 0
.x .. .x ..&#x  |  0  4 |  0  0  2  2 |  *  *  * 24  * | 0 1  0 1
.. .o3.x ..     |  0  3 |  0  0  0  3 |  *  *  *  * 16 | 0 0  1 1
----------------+-------+-------------+----------------+---------
.. x.3o.4o.       6  0 | 12  0  0  0 |  8  0  0  0  0 | 2 *  * *
wx .. ox4oo&#xt   2  8 |  0  8  4  8 |  0  0  8  4  0 | * 6  * *
.. xo3ox ..&#x    3  3 |  3  6  0  3 |  1  3  3  0  1 | * * 16 *
.x .o3.x ..&#x    0  6 |  0  0  3  6 |  0  0  0  3  2 | * *  * 8

(wx)(wx)(wx) (ox)(xo)(ox)4(oo)(oq)(oo)&#xt   → both heights = 1/sqrt(2) = 0.707107
(esquidpy || pseudo pexco || esquidpy)

(o.)(..)(..) (o.)(..)(..)4(o.)(..)(..)     & | 4  * * *   4  4 0  0  0  0 0  0 0 |  4  4  4 0  0  0  0 0 | 1 1  4 0 0
(.o)(..)(..) (.o)(..)(..)4(.o)(..)(..)     & | * 16 * * |  1  0 1  2  1  2 0  0 0 |  2  0  1 2  2  2  2 0 | 1 0  2 1 2
(..)(o.)(..) (..)(o.)(..)4(..)(o.)(..)       | *  * 8 *   0  2 0  0  2  0 2  2 0 |  0  4  2 0  0  0  4 2 | 0 1  4 1 0
(..)(.o)(..) (..)(.o)(..)4(..)(.o)(..)       | *  * * 8 |  0  0 0  0  0  4 0  2 1 |  0  0  0 0  4  2  4 1 | 0 0  2 2 2
---------------------------------------------+----------+-------------------------+-----------------------+-----------
(oo)(..)(..) (oo)(..)(..)4(oo)(..)(..)&#x  & | 1  1 0 0 | 16  * *  *  *  * *  * * |  2  0  1 0  0  0  0 0 | 1 0  2 0 0
(o.)(o.)(..) (o.)(o.)(..)4(o.)(o.)(..)&#x  & | 1  0 1 0 |  * 16 *  *  *  * *  * * |  0  2  1 0  0  0  0 0 | 0 1  2 0 0
(.x)(..)(..) (..)(..)(..) (..)(..)(..)     & | 0  2 0 0 |  *  * 8  *  *  * *  * * |  0  0  0 2  2  0  0 0 | 1 0  0 1 2
(..)(..)(..) (.x)(..)(..) (..)(..)(..)     & | 0  2 0 0 |  *  * * 16  *  * *  * * |  1  0  0 1  0  1  0 0 | 1 0  1 0 1
(.o)(o.)(..) (.o)(o.)(..)4(.o)(o.)(..)&#x  & | 0  1 1 0 |  *  * *  * 16  * *  * * |  0  0  1 0  0  0  2 0 | 0 0  2 1 0
(.o)(.o)(..) (.o)(.o)(..)4(.o)(.o)(..)&#x  & | 0  1 0 1 |  *  * *  *  * 32 *  * * |  0  0  0 0  1  1  1 0 | 0 0  1 1 1
(..)(..)(..) (..)(x.)(..) (..)(..)(..)       | 0  0 2 0 |  *  * *  *  *  * 8  * * |  0  2  0 0  0  0  0 1 | 0 1  2 0 0
(..)(oo)(..) (..)(oo)(..)4(..)(oo)(..)&#x    | 0  0 1 1 |  *  * *  *  *  * * 16 * |  0  0  0 0  0  0  2 1 | 0 0  2 1 0
(..)(.x)(..) (..)(..)(..) (..)(..)(..)       | 0  0 0 2 |  *  * *  *  *  * *  * 4 |  0  0  0 0  4  0  0 0 | 0 0  0 2 2
---------------------------------------------+----------+-------------------------+-----------------------+-----------
(..)(..)(..) (ox)(..)(..) (..)(..)(..)&#x  & | 1  2 0 0 |  2  0 0  1  0  0 0  0 0 | 16  *  * *  *  *  * * | 1 0  1 0 0
(..)(..)(..) (o.)(x.)(..) (..)(..)(..)&#x  & | 1  0 2 0 |  0  2 0  0  0  0 1  0 0 |  * 16  * *  *  *  * * | 0 1  1 0 0
(oo)(o.)(..) (oo)(o.)(..)4(oo)(o.)(..)&#x  & | 1  1 1 0 |  1  1 0  0  1  0 0  0 0 |  *  * 16 *  *  *  * * | 0 0  2 0 0
(.x)(..)(..) (.x)(..)(..) (..)(..)(..)     & | 0  4 0 0 |  0  0 2  2  0  0 0  0 0 |  *  *  * 8  *  *  * * | 1 0  0 0 1
(.x)(.x)(..) (..)(..)(..) (..)(..)(..)&#x  & | 0  2 0 2 |  0  0 1  0  0  2 0  0 1 |  *  *  * * 16  *  * * | 0 0  0 1 1
(..)(..)(..) (.x)(.o)(..) (..)(..)(..)&#x  & | 0  2 0 1 |  0  0 0  1  0  2 0  0 0 |  *  *  * *  * 16  * * | 0 0  2 0 0
(.o)(oo)(..) (.o)(oo)(..)4(.o)(oo)(..)&#x  & | 0  1 1 1 |  0  0 0  0  1  1 0  1 0 |  *  *  * *  *  * 32 * | 0 0  1 1 0
(..)(..)(..) (..)(xo)(..) (..)(..)(..)&#x    | 0  0 2 1 |  0  0 0  0  0  0 1  2 0 |  *  *  * *  *  *  * 8 | 0 0  2 0 0
---------------------------------------------+----------+-------------------------+-----------------------+-----------
(wx)(..)(..) (ox)(..)(..)4(oo)(..)(..)&#zx &  2  8 0 0 |  8  0 4  8  0  0 0  0 0 |  8  0  0 4  0  0  0 0 | 2 *  * * *
(..)(..)(..) (o.)(x.)(o.)4(o.)(o.)(o.)&#xt    2  0 4 0 |  0  8 0  0  0  0 4  0 0 |  0  8  0 0  0  0  0 0 | * 2  * * *
(..)(..)(..) (ox)(xo)(..) (..)(..)(..)&#xr &  1  2 2 1 |  2  2 0  1  2  2 1  2 0 |  1  1  2 0  0  1  2 1 | * * 16 * *
(.x)(wx)(.x) (..)(..)(..) (.o)(oq)(.o)&#xt    0  4 2 4 |  0  0 2  0  4  8 0  4 2 |  0  0  0 0  4  0  8 0 | * *  * 4 *
(.x)(.x)(..) (.x)(.o)(..) (..)(..)(..)&#x  &  0  4 0 2 |  0  0 2  2  0  4 0  0 1 |  0  0  0 1  2  2  0 0 | * *  * * 8

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