Acronym thexa (old: thexag thex), thex || gyro thex
Name thex alterprism,
thex atop gyro thex,
equatorial segment of sirhin
Circumradius sqrt(21/8) = 1.620185
Lace city
in approx. ASCII-art 
x3x3o  u3o3x  x3o3u  o3x3x
                          
                          
                          
o3x3x  x3o3u  u3o3x  x3x3o
Face vector 96, 336, 384, 168, 26
Confer
uniform relative:
sirhin  
general polytopal classes:
scaliform   segmentotera   lace simplices  
External
links 		polytopewiki  

Incidence matrix according to Dynkin symbol

xo3xx3ox *b3oo&#x   → height = 1/sqrt(2) = 0.707107
(thex || gyro thex)

o.3o.3o. *b3o.    | 48  * |  1  4  2  0  0 |  4  2  2  2  4  1  0  0  0 | 2 2 1  4  1  2  2 0 0 0 | 1 2 2 1 0
.o3.o3.o *b3.o    |  * 48 |  0  0  2  4  1 |  0  0  0  1  4  2  2  4  2 | 0 0 0  2  1  4  2 2 1 2 | 0 2 1 2 1
------------------+-------+----------------+----------------------------+-------------------------+----------
x. .. ..    ..    |  2  0 | 24  *  *  *  * |  4  0  0  2  0  0  0  0  0 | 2 2 0  4  1  0  0 0 0 0 | 1 2 2 0 0
.. x. ..    ..    |  2  0 |  * 96  *  *  * |  1  1  1  0  1  0  0  0  0 | 1 1 1  1  0  1  0 0 0 0 | 1 1 1 1 0
oo3oo3oo *b3oo&#x |  1  1 |  *  * 96  *  * |  0  0  0  1  2  1  0  0  0 | 0 0 0  2  1  2  1 0 0 0 | 0 2 1 1 0
.. .x ..    ..    |  0  2 |  *  *  * 96  * |  0  0  0  0  1  0  1  1  1 | 0 0 0  1  0  1  1 1 1 1 | 0 1 1 1 1
.. .. .x    ..    |  0  2 |  *  *  *  * 24 |  0  0  0  0  0  2  0  4  0 | 0 0 0  0  1  4  0 2 0 2 | 0 2 0 2 1
------------------+-------+----------------+----------------------------+-------------------------+----------
x.3x. ..    ..    |  6  0 |  3  3  0  0  0 | 32  *  *  *  *  *  *  *  * | 1 1 0  1  0  0  0 0 0 0 | 1 1 1 0 0
.. x.3o.    ..    |  3  0 |  0  3  0  0  0 |  * 32  *  *  *  *  *  *  * | 1 0 1  0  0  1  0 0 0 0 | 1 1 0 1 0
.. x. .. *b3o.    |  3  0 |  0  3  0  0  0 |  *  * 32  *  *  *  *  *  * | 0 1 1  0  0  0  1 0 0 0 | 1 0 1 1 0
xo .. ..    ..&#x |  2  1 |  1  0  2  0  0 |  *  *  * 48  *  *  *  *  * | 0 0 0  2  1  0  0 0 0 0 | 0 2 1 0 0
.. xx ..    ..&#x |  2  2 |  0  1  2  1  0 |  *  *  *  * 96  *  *  *  * | 0 0 0  1  0  1  1 0 0 0 | 0 1 1 1 0
.. .. ox    ..&#x |  1  2 |  0  0  2  0  1 |  *  *  *  *  * 48  *  *  * | 0 0 0  0  1  2  0 0 0 0 | 0 2 0 1 0
.o3.x ..    ..    |  0  3 |  0  0  0  3  0 |  *  *  *  *  *  * 32  *  * | 0 0 0  1  0  0  0 1 1 0 | 0 1 1 0 1
.. .x3.x    ..    |  0  6 |  0  0  0  3  3 |  *  *  *  *  *  *  * 32  * | 0 0 0  0  0  1  0 1 0 1 | 0 1 0 1 1
.. .x .. *b3.o    |  0  3 |  0  0  0  3  0 |  *  *  *  *  *  *  *  * 32 | 0 0 0  0  0  0  1 0 1 1 | 0 0 1 1 1
------------------+-------+----------------+----------------------------+-------------------------+----------
x.3x.3o.    ..    ♦ 12  0 |  6 12  0  0  0 |  4  4  0  0  0  0  0  0  0 | 8 * *  *  *  *  * * * * | 1 1 0 0 0
x.3x. .. *b3o.    ♦ 12  0 |  6 12  0  0  0 |  4  0  4  0  0  0  0  0  0 | * 8 *  *  *  *  * * * * | 1 0 1 0 0
.. x.3o. *b3o.    ♦  6  0 |  0 12  0  0  0 |  0  4  4  0  0  0  0  0  0 | * * 8  *  *  *  * * * * | 1 0 0 1 0
xo3xx ..    ..&#x ♦  6  3 |  3  3  6  3  0 |  1  0  0  3  3  0  1  0  0 | * * * 32  *  *  * * * * | 0 1 1 0 0
xo .. ox    ..&#x ♦  2  2 |  1  0  4  0  1 |  0  0  0  2  0  2  0  0  0 | * * *  * 24  *  * * * * | 0 2 0 0 0
.. xx3ox    ..&#x ♦  3  6 |  0  3  6  3  3 |  0  1  0  0  3  3  0  1  0 | * * *  *  * 32  * * * * | 0 1 0 1 0
.. xx .. *b3oo&#x ♦  3  3 |  0  3  3  3  0 |  0  0  1  0  3  0  0  0  1 | * * *  *  *  * 32 * * * | 0 0 1 1 0
.o3.x3.x    ..    ♦  0 12 |  0  0  0 12  6 |  0  0  0  0  0  0  4  4  0 | * * *  *  *  *  * 8 * * | 0 1 0 0 1
.o3.x .. *b3.o    ♦  0  6 |  0  0  0 12  0 |  0  0  0  0  0  0  4  0  4 | * * *  *  *  *  * * 8 * | 0 0 1 0 1
.. .x3.x *b3.o    ♦  0 12 |  0  0  0 12  6 |  0  0  0  0  0  0  0  4  4 | * * *  *  *  *  * * * 8 | 0 0 0 1 1
------------------+-------+----------------+----------------------------+-------------------------+----------
x.3x.3o. *b3o.    ♦ 48  0 | 24 96  0  0  0 | 32 32 32  0  0  0  0  0  0 | 8 8 8  0  0  0  0 0 0 0 | 1 * * * *
xo3xx3ox    ..&#x ♦ 12 12 |  6 12 24 12  6 |  4  4  0 12 12 12  4  4  0 | 1 0 0  4  6  4  0 1 0 0 | * 8 * * *
xo3xx .. *b3oo&#x ♦ 12  6 |  6 12 12 12  0 |  4  0  4  6 12  0  4  0  4 | 0 1 0  4  0  0  4 0 1 0 | * * 8 * *
.. xx3ox *b3oo&#x ♦  6 12 |  0 12 12 12  6 |  0  4  4  0 12  6  0  4  4 | 0 0 1  0  0  4  4 0 0 1 | * * * 8 *
.o3.x3.x *b3.o    ♦  0 48 |  0  0  0 96 24 |  0  0  0  0  0  0 32 32 32 | 0 0 0  0  0  0  0 8 8 8 | * * * * 1

or
o.3o.3o. *b3o.    & | 96 |  1   4  2 |  4  2  2  3  4 |  2  2  1  6  1  2 | 1 2  3
--------------------+----+-----------+----------------+-------------------+-------
x. .. ..    ..    & |  2 | 48   *  * |  4  0  0  2  0 |  2  2  0  4  1  0 | 1 2  2
.. x. ..    ..    & |  2 |  * 192  * |  1  1  1  0  1 |  1  1  1  2  0  1 | 1 1  2
oo3oo3oo *b3oo&#x   |  2 |  *   * 96 |  0  0  0  2  2 |  0  0  0  4  1  1 | 0 2  2
--------------------+----+-----------+----------------+-------------------+-------
x.3x. ..    ..    & |  6 |  3   3  0 | 64  *  *  *  * |  1  1  0  1  0  0 | 1 1  1
.. x.3o.    ..    & |  3 |  0   3  0 |  * 64  *  *  * |  1  0  1  1  0  0 | 1 1  1
.. x. .. *b3o.    & |  3 |  0   3  0 |  *  * 64  *  * |  0  1  1  0  0  1 | 1 0  2
xo .. ..    ..&#x & |  3 |  1   0  2 |  *  *  * 96  * |  0  0  0  2  1  0 | 0 2  1
.. xx ..    ..&#x   |  4 |  0   2  2 |  *  *  *  * 96 |  0  0  0  2  0  1 | 0 1  2
--------------------+----+-----------+----------------+-------------------+-------
x.3x.3o.    ..    & ♦ 12 |  6  12  0 |  4  4  0  0  0 | 16  *  *  *  *  * | 1 1  0
x.3x. .. *b3o.    & ♦ 12 |  6  12  0 |  4  0  4  0  0 |  * 16  *  *  *  * | 1 0  1
.. x.3o. *b3o.    & ♦  6 |  0  12  0 |  0  4  4  0  0 |  *  * 16  *  *  * | 1 0  1
xo3xx ..    ..&#x & ♦  9 |  3   6  6 |  1  1  0  3  3 |  *  *  * 64  *  * | 0 1  1
xo .. ox    ..&#x   ♦  4 |  2   0  4 |  0  0  0  4  0 |  *  *  *  * 24  * | 0 2  0
.. xx .. *b3oo&#x   ♦  6 |  0   6  3 |  0  0  2  0  3 |  *  *  *  *  * 32 | 0 0  2
--------------------+----+-----------+----------------+-------------------+-------
x.3x.3o. *b3o.    & ♦ 48 | 24  96  0 | 32 32 32  0  0 |  8  8  8  0  0  0 | 2 *  *
xo3xx3ox    ..&#x   ♦ 24 | 12  24 24 |  8  8  0 24 12 |  2  0  0  8  6  0 | * 8  *
xo3xx .. *b3oo&#x & ♦ 18 |  6  24 12 |  4  4  8  6 12 |  0  1  1  4  0  4 | * * 16


s2o3x3o4s

demi( . . . . . ) | 96 |   4  2  1 |  2  2  4  3  4 |  1  2  1  2  6  2 | 2 1  3
------------------+----+-----------+----------------+-------------------+-------
demi( . . x . . ) |  2 | 192  *  * |  1  1  1  0  1 |  1  1  0  1  2  1 | 1 1  2
      s . 2 . s   |  2 |   * 96  * |  0  0  2  2  0 |  0  1  1  0  4  0 | 2 0  2
      . . . o4s   |  2 |   *  * 48 |  0  0  0  2  4 |  0  0  1  2  4  2 | 2 1  2
------------------+----+-----------+----------------+-------------------+-------
demi( . o3x . . ) |  3 |   3  0  0 | 64  *  *  *  * |  1  1  0  0  0  1 | 0 1  2
demi( . . x3o . ) |  3 |   3  0  0 |  * 64  *  *  * |  1  0  0  1  1  0 | 1 1  1
      s 2 x 2 s   |  4 |   2  2  0 |  *  * 96  *  * |  0  1  0  0  2  0 | 1 0  2
sefa( s . 2 o4s ) |  3 |   0  2  1 |  *  *  * 96  * |  0  0  1  0  2  0 | 2 0  1
sefa( . . x3o4s ) |  6 |   3  0  3 |  *  *  *  * 64 |  0  0  0  1  1  1 | 1 1  1
------------------+----+-----------+----------------+-------------------+-------
demi( . o3x3o . ) ♦  6 |  12  0  0 |  4  4  0  0  0 | 16  *  *  *  *  * | 0 1  1
      s2o3x 2 s   ♦  6 |   6  3  0 |  2  0  3  0  0 |  * 32  *  *  *  * | 0 0  2
      s . 2 o4s   ♦  4 |   0  4  2 |  0  0  0  4  0 |  *  * 24  *  *  * | 2 0  0
      . . x3o4s   ♦ 12 |  12  0  6 |  0  4  0  0  4 |  *  *  * 16  *  * | 1 1  0
sefa( s 2 x3o4s ) ♦  9 |   6  6  3 |  0  1  3  3  1 |  *  *  *  * 64  * | 1 0  1
sefa( . o3x3o4s ) ♦ 12 |  12  0  6 |  4  0  0  0  4 |  *  *  *  *  * 16 | 0 1  1
------------------+----+-----------+----------------+-------------------+-------
      s 2 x3o4s   ♦ 24 |  24 24 12 |  0  8 12 24  8 |  0  0  6  2  8  0 | 8 *  *
      . o3x3o4s   ♦ 48 |  96  0 24 | 32 32  0  0 32 |  8  0  0  8  0  8 | * 2  *
sefa( s2o3x3o4s ) ♦ 18 |  24 12  6 |  8  4 12  6  4 |  1  4  0  0  4  1 | * * 16

starting figure: x o3x3o4x

© 2004-2024
top of page