Acronym pex hex
Name partially (mono-)expanded hex,
partially contracted quawros
Lace city
in approx. ASCII-art
    o4o   o4o    
                 
o4o o4x   o4x o4o
                 
    o4o   o4o    
    x3o   x3o    
o3o           o3o
    o3x   o3x    
Dihedral angles
  • at {3} between tet and trip:   150°
  • at {3} between tet and tet:   120°
  • at {4} between trip and trip:   arccos(-1/3) = 109.471221°
Confer
uniform relative:
hex   sidpith  
related CRFs:
quawros   pacsid pith   esquippidpy   eoctpy  
general polytopal classes:
partial Stott expansions   bistratic lace towers  

Incidence matrix according to Dynkin symbol

oxxo3oooo4oooo&#xt   → outer heights = 1/sqrt(2) = 0.707107
                       inner height = 1
(point || pseudo oct || pseudo oct || point)

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

o(ox)o4o(oo)o x(wx)x&#xt   → both heights = 1/sqrt(2) = 0.707107
(line || pseudo esquidpy || line)

o(..).4o(..). o(..).     & | 4 * * | 1 1  4 0 0 0 |  4  4 4 0 0 |  4 4
.(o.).4.(o.). .(o.).       | * 2 *  0 2  0 4 0 0 |  8  0 0 4 0 |  8 0
.(.o).4.(.o). .(.o).       | * * 8 | 0 0  2 1 2 1 |  2  4 2 2 4 |  4 4
---------------------------+-------+--------------+-------------+-----
.(..). .(..). x(..).     & | 2 0 0 | 2 *  * * * * |  0  0 4 0 0 |  0 4
o(o.).4o(o.). o(o.).&#x  & | 1 1 0 | * 4  * * * * |  4  0 0 0 0 |  4 0
o(.o).4o(.o). o(.o).&#x  & | 1 0 1 | * * 16 * * * |  1  2 1 0 0 |  2 2
.(oo).4.(oo). .(oo).&#x    | 0 1 1 | * *  * 8 * * |  2  0 0 2 0 |  4 0
.(.x). .(..). .(..).       | 0 0 2 | * *  * * 8 * |  0  2 0 1 1 |  2 2
.(..). .(..). .(.x).       | 0 0 2 | * *  * * * 4 |  0  0 2 0 2 |  0 4
---------------------------+-------+--------------+-------------+-----
o(oo).4o(oo). o(oo).&#x  & | 1 1 1 | 0 1  1 1 0 0 | 16  * * * * |  2 0
o(.x). .(..). .(..).&#x  & | 1 0 2 | 0 0  2 0 1 0 |  * 16 * * * |  1 1
.(..). .(..). x(.x).&#x  & | 2 0 2 | 1 0  2 0 0 1 |  *  * 8 * * |  0 2
.(ox). .(..). .(..).&#x    | 0 1 2 | 0 0  0 2 1 0 |  *  * * 8 * |  2 0
.(.x). .(..). .(.x).       | 0 0 4 | 0 0  0 0 2 2 |  *  * * * 4 |  0 2
---------------------------+-------+--------------+-------------+-----
o(ox). .(..). .(..).&#x  &  1 1 2 | 0 1  2 2 1 0 |  2  1 0 1 0 | 16 *
o(.x). .(..). x(.x).&#x  &  2 0 4 | 1 0  4 0 2 2 |  0  2 2 0 1 |  * 8

o(qoo)o o(oqo)o x(xxw)x&#xt   → both heights = 1/sqrt(2) = 0.707107
(line || pseudo esquidpy || line)

o(...). o(...). o(...).    | 2 * * * * | 1 2 2 1 0 0 0 0 0 0 0 0 0 | 2 2 4 2 2 0 0 0 0 0 0 0 | 4 4 0 0
.(o..). .(o..). .(o..).    | * 4 * * * | 0 1 0 0 1 2 1 1 0 0 0 0 0 | 1 0 2 1 0 2 2 1 2 1 0 0 | 2 2 2 2
.(.o.). .(.o.). .(.o.).    | * * 4 * * | 0 0 1 0 0 2 0 0 1 1 1 0 0 | 0 1 2 0 1 2 2 0 2 0 1 1 | 2 2 2 2
.(..o). .(..o). .(..o).    | * * * 2 *  0 0 0 1 0 0 2 0 0 2 0 1 0 | 0 0 0 2 2 0 4 0 0 2 0 2 | 0 4 0 4
.(...)o .(...)o .(...)o    | * * * * 2 | 0 0 0 0 0 0 0 2 0 0 2 1 1 | 0 0 0 0 0 0 0 2 4 2 2 2 | 0 0 4 4
---------------------------+-----------+---------------------------+-------------------------+--------
.(...). .(...). x(...).    | 2 0 0 0 0 | 1 * * * * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 0 | 4 0 0 0
o(o..). o(o..). o(o..).&#x | 1 1 0 0 0 | * 4 * * * * * * * * * * * | 1 0 2 1 0 0 0 0 0 0 0 0 | 2 2 0 0
o(.o.). o(.o.). o(.o.).&#x | 1 0 1 0 0 | * * 4 * * * * * * * * * * | 0 1 2 0 1 0 0 0 0 0 0 0 | 2 2 0 0
o(..o). o(..o). o(..o).&#x | 1 0 0 1 0 | * * * 2 * * * * * * * * * | 0 0 0 2 2 0 0 0 0 0 0 0 | 0 4 0 0
.(...). .(...). .(x..).    | 0 2 0 0 0 | * * * * 2 * * * * * * * * | 1 0 0 0 0 2 0 1 0 0 0 0 | 2 0 2 0
.(oo.). .(oo.). .(oo.).&#x | 0 1 1 0 0 | * * * * * 8 * * * * * * * | 0 0 1 0 0 1 1 0 1 0 0 0 | 1 1 1 1
.(o.o). .(o.o). .(o.o).&#x | 0 1 0 1 0 | * * * * * * 4 * * * * * * | 0 0 0 1 0 0 2 0 0 1 0 0 | 0 2 0 2
.(o..)o .(o..)o .(o..)o&#x | 0 1 0 0 1 | * * * * * * * 4 * * * * * | 0 0 0 0 0 0 0 1 2 1 0 0 | 0 0 2 2
.(...). .(...). .(.x.).    | 0 0 2 0 0 | * * * * * * * * 2 * * * * | 0 1 0 0 0 2 0 0 0 0 1 0 | 2 0 2 0
.(.oo). .(.oo). .(.oo).&#x | 0 0 1 1 0 | * * * * * * * * * 4 * * * | 0 0 0 0 1 0 2 0 0 0 0 1 | 0 2 0 2
.(.o.)o .(.o.)o .(.o.)o&#x | 0 0 1 0 1 | * * * * * * * * * * 4 * * | 0 0 0 0 0 0 0 0 2 0 1 1 | 0 0 2 2
.(..o)o .(..o)o .(..o)o&#x | 0 0 0 1 1 | * * * * * * * * * * * 2 * | 0 0 0 0 0 0 0 0 0 2 0 2 | 0 0 0 4
.(...). .(...). .(...)x    | 0 0 0 0 2 | * * * * * * * * * * * * 1 | 0 0 0 0 0 0 0 2 0 0 2 0 | 0 0 4 0
---------------------------+-----------+---------------------------+-------------------------+--------
.(...). .(...). x(x..).&#x | 2 2 0 0 0 | 1 2 0 0 1 0 0 0 0 0 0 0 0 | 2 * * * * * * * * * * * | 2 0 0 0
.(...). .(...). x(.x.).&#x | 2 0 2 0 0 | 1 0 2 0 0 0 0 0 1 0 0 0 0 | * 2 * * * * * * * * * * | 2 0 0 0
o(oo.). o(oo.). o(oo.).&#x | 1 1 1 0 0 | 0 1 1 0 0 1 0 0 0 0 0 0 0 | * * 8 * * * * * * * * * | 1 1 0 0
o(o.o). o(o.o). o(o.o).&#x | 1 1 0 1 0 | 0 1 0 1 0 0 1 0 0 0 0 0 0 | * * * 4 * * * * * * * * | 0 2 0 0
o(.oo). o(.oo). o(.oo).&#x | 1 0 1 1 0 | 0 0 1 1 0 0 0 0 0 1 0 0 0 | * * * * 4 * * * * * * * | 0 2 0 0
.(...). .(...). .(xx.).&#x | 0 2 2 0 0 | 0 0 0 0 1 2 0 0 1 0 0 0 0 | * * * * * 4 * * * * * * | 1 0 1 0
.(ooo). .(ooo). .(ooo).&#x | 0 1 1 1 0 | 0 0 0 0 0 1 1 0 0 1 0 0 0 | * * * * * * 8 * * * * * | 0 1 0 1
.(...). .(...). .(x..)x&#x | 0 2 0 0 2 | 0 0 0 0 1 0 0 2 0 0 0 0 1 | * * * * * * * 2 * * * * | 0 0 2 0
.(oo.)o .(oo.)o .(oo.)o&#x | 0 1 1 0 1 | 0 0 0 0 0 1 0 1 0 0 1 0 0 | * * * * * * * * 8 * * * | 0 0 1 1
.(o.o)o .(o.o)o .(o.o)o&#x | 0 1 0 1 1 | 0 0 0 0 0 0 1 1 0 0 0 1 0 | * * * * * * * * * 4 * * | 0 0 0 2
.(...). .(...). .(.x.)x&#x | 0 0 2 0 2 | 0 0 0 0 0 0 0 0 1 0 2 0 1 | * * * * * * * * * * 2 * | 0 0 2 0
.(.oo)o .(.oo)o .(.oo)o&#x | 0 0 1 1 1 | 0 0 0 0 0 0 0 0 0 1 1 1 0 | * * * * * * * * * * * 4 | 0 0 0 2
---------------------------+-----------+---------------------------+-------------------------+--------
.(...). .(...). x(xx.).&#x  2 2 2 0 0 | 1 2 2 0 1 2 0 0 1 0 0 0 0 | 1 1 2 0 0 1 0 0 0 0 0 0 | 4 * * *
o(ooo). o(ooo). o(ooo).&#x  1 1 1 1 0 | 0 1 1 1 0 1 1 0 0 1 0 0 0 | 0 0 1 1 1 0 1 0 0 0 0 0 | * 8 * *
.(...). .(...). .(xx.)x&#x  0 2 2 0 2 | 0 0 0 0 1 2 0 2 1 0 2 0 1 | 0 0 0 0 0 1 0 1 2 0 1 0 | * * 4 *
.(ooo)o .(ooo)o .(ooo)o&#x  0 1 1 1 1 | 0 0 0 0 0 1 1 1 0 1 1 1 0 | 0 0 0 0 0 0 1 0 1 1 0 1 | * * * 8

oox3xoo xwx&#xt   → both heights = 1/sqrt(6) = 0.408248
(trip || pseudo w-line || inv trip)

o..3o.. o..     & | 12 * |  2 1  1  2 | 1 2  2  3 2  2 | 1 1 3  3
.o.3.o. .o.       |  * 2   0 0  6  0 | 0 0  6  0 0  6 | 0 2 0  6
------------------+------+------------+----------------+---------
... x.. ...     & |  2 0 | 12 *  *  * | 1 1  1  1 0  0 | 1 1 1  1
... ... x..     & |  2 0 |  * 6  *  * | 0 2  0  0 2  0 | 1 0 3  0
oo.3oo. oo.&#x  & |  1 1 |  * * 12  * | 0 0  2  0 0  2 | 0 1 0  3
o.o3o.o o.o&#x    |  2 0 |  * *  * 12 | 0 0  0  2 1  1 | 0 0 2  2
------------------+------+------------+----------------+---------
o..3x.. ...     & |  3 0 |  3 0  0  0 | 4 *  *  * *  * | 1 1 0  0
... x.. x..     & |  4 0 |  2 2  0  0 | * 6  *  * *  * | 1 0 1  0
... xo. ...&#x  & |  2 1 |  1 0  2  0 | * * 12  * *  * | 0 1 0  1
o.x ... ...&#x  & |  3 0 |  1 0  0  2 | * *  * 12 *  * | 0 0 1  1
... ... x.x&#x    |  4 0 |  0 2  0  2 | * *  *  * 6  * | 0 0 2  0
ooo3ooo ooo&#x    |  2 1 |  0 0  2  1 | * *  *  * * 12 | 0 0 0  2
------------------+------+------------+----------------+---------
o..3x.. x..     &   6 0 |  6 3  0  0 | 2 3  0  0 0  0 | 2 * *  *
oo.3xo. ...&#x  &   3 1 |  3 0  3  0 | 1 0  3  0 0  0 | * 4 *  *
o.x ... x.x&#x  &   6 0 |  2 3  0  4 | 0 1  0  2 2  0 | * * 6  *
oox ... ...&#x  &   3 1 |  1 0  3  2 | 0 0  1  1 0  2 | * * * 12

wx ox3oo4oo&#zx   → height = 0
(tegum sum of w-line and ope)

o. o.3o.4o.     | 2  *   6 0  0 | 12  0  0 |  8 0
.o .o3.o4.o     | * 12 |  1 1  4 |  4  4  4 |  4 4
----------------+------+---------+----------+-----
oo oo3oo4oo&#x  | 1  1 | 12 *  * |  4  0  0 |  4 0
.x .. .. ..     | 0  2 |  * 6  * |  0  4  0 |  0 4
.. .x .. ..     | 0  2 |  * * 24 |  1  1  2 |  2 2
----------------+------+---------+----------+-----
.. ox .. ..&#x  | 1  2 |  2 0  1 | 24  *  * |  2 0
.x .x .. ..     | 0  4 |  0 2  2 |  * 12  * |  0 2
.. .x3.o ..     | 0  3 |  0 0  3 |  *  * 16 |  1 1
----------------+------+---------+----------+-----
.. ox3oo ..&#x   1  3 |  3 0  3 |  3  0  1 | 16 *
.x .x3.o ..      0  6 |  0 3  6 |  0  3  2 |  * 8

wxxx oqoo ooqo oooq&#zx   → height = 0
(tegum sum of w-line and 3 ortho (q,x)-{4})

o... o... o... o...     | 2 * * *  2 2 2 0 0 0 0 0 0 | 4 4 4 0 0  0 0 |  8 0
.o.. .o.. .o.. .o..     | * 4 * * | 1 0 0 1 2 2 0 0 0 | 2 2 0 2 2  4 0 |  4 4
..o. ..o. ..o. ..o.     | * * 4 * | 0 1 0 0 2 0 1 2 0 | 2 0 2 2 0  4 2 |  4 4
...o ...o ...o ...o     | * * * 4 | 0 0 1 0 0 2 0 2 1 | 0 2 2 0 2  4 2 |  4 4
------------------------+---------+-------------------+----------------+-----
oo.. oo.. oo.. oo..&#x  | 1 1 0 0 | 4 * * * * * * * * | 2 2 0 0 0  0 0 |  4 0
o.o. o.o. o.o. o.o.&#x  | 1 0 1 0 | * 4 * * * * * * * | 2 0 2 0 0  0 0 |  4 0
o..o o..o o..o o..o&#x  | 1 0 0 1 | * * 4 * * * * * * | 0 2 2 0 0  0 0 |  4 0
.x.. .... .... ....     | 0 2 0 0 | * * * 2 * * * * * | 0 0 0 2 2  0 0 |  0 4
.oo. .oo. .oo. .oo.&#x  | 0 1 1 0 | * * * * 8 * * * * | 1 0 0 1 0  2 0 |  2 2
.o.o .o.o .o.o .o.o&#x  | 0 1 0 1 | * * * * * 8 * * * | 0 1 0 0 1  2 0 |  2 2
..x. .... .... ....     | 0 0 2 0 | * * * * * * 2 * * | 0 0 0 2 0  0 2 |  0 4
..oo ..oo ..oo ..oo&#x  | 0 0 1 1 | * * * * * * * 8 * | 0 0 1 0 0  2 1 |  2 2
...x .... .... ....     | 0 0 0 2 | * * * * * * * * 2 | 0 0 0 0 2  0 2 |  0 4
------------------------+---------+-------------------+----------------+-----
ooo. ooo. ooo. ooo.&#x  | 1 1 1 0 | 1 1 0 0 1 0 0 0 0 | 8 * * * *  * * |  2 0
oo.o oo.o oo.o oo.o&#x  | 1 1 0 1 | 1 0 1 0 0 1 0 0 0 | * 8 * * *  * * |  2 0
o.oo o.oo o.oo o.oo&#x  | 1 0 1 1 | 0 1 1 0 0 0 0 1 0 | * * 8 * *  * * |  2 0
.xx. .... .... ....&#x  | 0 2 2 0 | 0 0 0 1 2 0 1 0 0 | * * * 4 *  * * |  0 2
.x.x .... .... ....&#x  | 0 2 0 2 | 0 0 0 1 0 2 0 0 1 | * * * * 4  * * |  0 2
.ooo .ooo .ooo .ooo&#x  | 0 1 1 1 | 0 0 0 0 1 1 0 1 0 | * * * * * 16 * |  1 1
..xx .... .... ....&#x  | 0 0 2 2 | 0 0 0 0 0 0 1 2 1 | * * * * *  * 4 |  0 2
------------------------+---------+-------------------+----------------+-----
oooo oooo oooo oooo&#x   1 1 1 1 | 1 1 1 0 1 1 0 1 0 | 1 1 1 0 0  1 0 | 16 *
.xxx .... .... ....&#x   0 2 2 2 | 0 0 0 1 2 2 1 2 1 | 0 0 0 1 1  2 1 |  * 8

© 2004-2018
top of page