Acronym	spix
Name	small prismated hexateron, runcinated hexateron
Field of sections	©
Circumradius	sqrt(17/12) = 1.190238
Lace city in approx. ASCII-art	_+-------------------- x o3x3o (ope) _/ _+-------------- uo ox3ox3xo _/ _/ _+-------- x x3o3x (cope) _/ _/ _/ _+-- o x3o3o (tet) _/ _/ _/ _/ o3x3o o3o3x -- o3x3o3o (rap) o3x3o x3x3o x3o3x -- o3x3o3x (inv. srip) o3o3x x3o3x x3o3o -- x3o3o3x (spid)
Lace hyper city in approx. ASCII-art	©   +----------------------------------------------------------- o x3o3o (tet) / +---------------------------------------- x x3o3x (cope) / / +--------------------- uo ox3ox3xo / / / +-- x o3x3o (ope) / / / / o top point of rap x x x medial inv. trip of rap o o o bottom {3} of rap o o o top {3} of inv. srip x x x x x x upper hip of inv. srip o u u o u o lower uo ou3xo of inv. srip x x x bottom trip of inv. srip x x x top trip of spid o o o u o o o medial uo ox3ox of spid x x x bottom inv. trip of spid \ \ \ \ \ \ \ +-- x3o x3o (triddip) \ \ +-------------------- ox3ox uo3ox \ +-------------------------------------- uo3ox ox3ox +-------------------------------------------------------- x3o x3o (triddip)
Vertex figure	©   ©
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – uniform polyteral members: by cells: chope duhd garpop ope rap rawvtip spid triddip topax 15 0 6 0 0 0 0 0 rippix 0 6 0 0 6 6 0 0 spix 0 0 0 15 6 0 6 20 & others)
Dihedral angles (at margins)	at trip between ope and triddip:   135° at oct between ope and rap:   arccos[-sqrt(2/5)] = 129.231520° at trip between spid and triddip:   arccos(-1/sqrt(5)) = 116.565051° at trip between ope and spid:   arccos[-sqrt(5)/8] = 106.230872° at tet between rap and spid:   arccos(-1/5) = 101.536959° at tet between spid and spid:   arccos(1/5) = 78.463041°
Face vector	60, 270, 420, 255, 47
Confer	related segmentotera: tetacope   rapalsrip   copatut   rapatut   spidasrip   triddipa hip   tripa thiddip   general polytopal classes: Wythoffian polytera   lace simplices
External links

Incidence matrix according to Dynkin symbol

x3o3o3x3o

. . . . . | 60 ♦  3   6 |  3  12   6  3 |  1  6  6  6  2  3 | 2  3  3 1
----------+----+--------+---------------+-------------------+----------
x . . . . |  2 | 90   * |  2   4   0  0 |  1  4  2  2  0  0 | 2  2  1 0
. . . x . |  2 |  * 180 |  0   2   2  1 |  0  1  2  2  1  2 | 1  1  2 1
----------+----+--------+---------------+-------------------+----------
x3o . . . |  3 |  3   0 | 60   *   *  * |  1  2  0  0  0  0 | 2  1  0 0
x . . x . |  4 |  2   2 |  * 180   *  * |  0  1  1  1  0  0 | 1  1  1 0
. . o3x . |  3 |  0   3 |  *   * 120  * |  0  0  1  0  1  1 | 1  0  1 1
. . . x3o |  3 |  0   3 |  *   *   * 60 |  0  0  0  2  0  2 | 0  1  2 1
----------+----+--------+---------------+-------------------+----------
x3o3o . . ♦  4 |  6   0 |  4   0   0  0 | 15  *  *  *  *  * | 2  0  0 0
x3o . x . ♦  6 |  6   3 |  2   3   0  0 |  * 60  *  *  *  * | 1  1  0 0
x . o3x . ♦  6 |  3   6 |  0   3   2  0 |  *  * 60  *  *  * | 1  0  1 0
x . . x3o ♦  6 |  3   6 |  0   3   0  2 |  *  *  * 60  *  * | 0  1  1 0
. o3o3x . ♦  4 |  0   6 |  0   0   4  0 |  *  *  *  * 30  * | 1  0  0 1
. . o3x3o ♦  6 |  0  12 |  0   0   4  4 |  *  *  *  *  * 30 | 0  0  1 1
----------+----+--------+---------------+-------------------+----------
x3o3o3x . ♦ 20 | 30  30 | 20  30  20  0 |  5 10 10  0  5  0 | 6  *  * *
x3o . x3o ♦  9 |  9   9 |  3   9   0  3 |  0  3  0  3  0  0 | * 20  * *
x . o3x3o ♦ 12 |  6  24 |  0  12   8  8 |  0  0  4  4  0  2 | *  * 15 *
. o3o3x3o ♦ 10 |  0  30 |  0   0  20 10 |  0  0  0  0  5  5 | *  *  * 6

x3o3o3x3/2o

. . . .   . | 60 ♦  3   6 |  3  12   6  3 |  1  6  6  6  2  3 | 2  3  3 1
------------+----+--------+---------------+-------------------+----------
x . . .   . |  2 | 90   * |  2   4   0  0 |  1  4  2  2  0  0 | 2  2  1 0
. . . x   . |  2 |  * 180 |  0   2   2  1 |  0  1  2  2  1  2 | 1  1  2 1
------------+----+--------+---------------+-------------------+----------
x3o . .   . |  3 |  3   0 | 60   *   *  * |  1  2  0  0  0  0 | 2  1  0 0
x . . x   . |  4 |  2   2 |  * 180   *  * |  0  1  1  1  0  0 | 1  1  1 0
. . o3x   . |  3 |  0   3 |  *   * 120  * |  0  0  1  0  1  1 | 1  0  1 1
. . . x3/2o |  3 |  0   3 |  *   *   * 60 |  0  0  0  2  0  2 | 0  1  2 1
------------+----+--------+---------------+-------------------+----------
x3o3o .   . ♦  4 |  6   0 |  4   0   0  0 | 15  *  *  *  *  * | 2  0  0 0
x3o . x   . ♦  6 |  6   3 |  2   3   0  0 |  * 60  *  *  *  * | 1  1  0 0
x . o3x   . ♦  6 |  3   6 |  0   3   2  0 |  *  * 60  *  *  * | 1  0  1 0
x . . x3/2o ♦  6 |  3   6 |  0   3   0  2 |  *  *  * 60  *  * | 0  1  1 0
. o3o3x   . ♦  4 |  0   6 |  0   0   4  0 |  *  *  *  * 30  * | 1  0  0 1
. . o3x3/2o ♦  6 |  0  12 |  0   0   4  4 |  *  *  *  *  * 30 | 0  0  1 1
------------+----+--------+---------------+-------------------+----------
x3o3o3x   . ♦ 20 | 30  30 | 20  30  20  0 |  5 10 10  0  5  0 | 6  *  * *
x3o . x3/2o ♦  9 |  9   9 |  3   9   0  3 |  0  3  0  3  0  0 | * 20  * *
x . o3x3/2o ♦ 12 |  6  24 |  0  12   8  8 |  0  0  4  4  0  2 | *  * 15 *
. o3o3x3/2o ♦ 10 |  0  30 |  0   0  20 10 |  0  0  0  0  5  5 | *  *  * 6

oox3xxo3ooo3oxx&#xt   → both heights = sqrt(3/5) = 0.774597
(rap || inv pseudo srip || spid)

o..3o..3o..3o..     | 10  *  * |  6  3  0  0  0  0  0 |  3  6 12  3  0  0  0  0  0  0  0  0  0  0 | 3 2  6  6  6  1 0  0  0  0  0  0  0 0  0  0 0 | 1 3  3 2 0  0  0 0
.o.3.o.3.o.3.o.     |  * 30  * |  0  1  4  2  2  0  0 |  0  0  4  2  2  2  4  1  1  4  4  0  0  0 | 0 0  2  2  4  1 1  2  2  2  2  4  2 0  0  0 0 | 0 1  2 2 1  2  1 0
..o3..o3..o3..o     |  *  * 20 |  0  0  0  0  3  3  3 |  0  0  0  0  0  0  0  0  3  3  6  3  6  3 | 0 0  0  0  0  0 0  0  3  6  1  3  3 1  3  3 1 | 0 0  0 1 1  3  3 1
--------------------+----------+----------------------+-------------------------------------------+-----------------------------------------------+-------------------
... x.. ... ...     |  2  0  0 | 30  *  *  *  *  *  * |  1  2  2  0  0  0  0  0  0  0  0  0  0  0 | 2 1  2  2  1  0 0  0  0  0  0  0  0 0  0  0 0 | 1 2  1 1 0  0  0 0
oo.3oo.3oo.3oo.&#x  |  1  1  0 |  * 30  *  *  *  *  * |  0  0  4  2  0  0  0  0  0  0  0  0  0  0 | 0 0  2  2  4  1 0  0  0  0  0  0  0 0  0  0 0 | 0 1  2 2 0  0  0 0
... .x. ... ...     |  0  2  0 |  *  * 60  *  *  *  * |  0  0  1  0  1  1  1  0  0  2  0  0  0  0 | 0 0  1  1  1  0 1  1  1  0  1  1  0 0  0  0 0 | 0 1  1 1 1  1  0 0
... ... ... .x.     |  0  2  0 |  *  *  * 30  *  *  * |  0  0  0  1  0  0  2  1  0  0  2  0  0  0 | 0 0  0  0  2  1 0  1  0  1  0  2  2 0  0  0 0 | 0 0  1 2 0  1  1 0
.oo3.oo3.oo3.oo&#x  |  0  1  1 |  *  *  *  * 60  *  * |  0  0  0  0  0  0  0  0  1  2  2  0  0  0 | 0 0  0  0  0  0 0  0  2  2  1  2  1 0  0  0 0 | 0 0  0 1 1  2  1 0
..x ... ... ...     |  0  0  2 |  *  *  *  *  * 30  * |  0  0  0  0  0  0  0  0  1  0  0  2  2  0 | 0 0  0  0  0  0 0  0  2  2  0  0  0 1  2  1 0 | 0 0  0 0 1  2  1 1
... ... ... ..x     |  0  0  2 |  *  *  *  *  *  * 30 |  0  0  0  0  0  0  0  0  0  0  2  0  2  2 | 0 0  0  0  0  0 0  0  0  2  0  1  2 0  1  2 1 | 0 0  0 1 0  1  2 1
--------------------+----------+----------------------+-------------------------------------------+-----------------------------------------------+-------------------
o..3x.. ... ...     |  3  0  0 |  3  0  0  0  0  0  0 | 10  *  *  *  *  *  *  *  *  *  *  *  *  * | 2 0  2  0  0  0 0  0  0  0  0  0  0 0  0  0 0 | 1 2  1 0 0  0  0 0
... x..3o.. ...     |  3  0  0 |  3  0  0  0  0  0  0 |  * 20  *  *  *  *  *  *  *  *  *  *  *  * | 1 1  0  1  0  0 0  0  0  0  0  0  0 0  0  0 0 | 1 1  0 1 0  0  0 0
... xx. ... ...&#x  |  2  2  0 |  1  2  1  0  0  0  0 |  *  * 60  *  *  *  *  *  *  *  *  *  *  * | 0 0  1  1  1  0 0  0  0  0  0  0  0 0  0  0 0 | 0 1  1 1 0  0  0 0
... ... ... ox.&#x  |  1  2  0 |  0  2  0  1  0  0  0 |  *  *  * 30  *  *  *  *  *  *  *  *  *  * | 0 0  0  0  2  1 0  0  0  0  0  0  0 0  0  0 0 | 0 0  1 2 0  0  0 0
.o.3.x. ... ...     |  0  3  0 |  0  0  3  0  0  0  0 |  *  *  *  * 20  *  *  *  *  *  *  *  *  * | 0 0  1  0  0  0 1  1  1  0  0  0  0 0  0  0 0 | 0 1  1 0 1  0  0 0
... .x.3.o. ...     |  0  3  0 |  0  0  3  0  0  0  0 |  *  *  *  *  * 20  *  *  *  *  *  *  *  * | 0 0  0  1  0  0 1  0  0  0  1  0  0 0  0  0 0 | 0 1  0 1 1  0  0 0
... .x. ... .x.     |  0  4  0 |  0  0  2  2  0  0  0 |  *  *  *  *  *  * 30  *  *  *  *  *  *  * | 0 0  0  0  1  0 0  1  0  0  0  1  0 0  0  0 0 | 0 0  1 1 0  1  0 0
... ... .o.3.x.     |  0  3  0 |  0  0  0  3  0  0  0 |  *  *  *  *  *  *  * 10  *  *  *  *  *  * | 0 0  0  0  0  1 0  0  0  0  0  0  2 0  0  0 0 | 0 0  0 2 0  0  1 0
.ox ... ... ...&#x  |  0  1  2 |  0  0  0  0  2  1  0 |  *  *  *  *  *  *  *  * 30  *  *  *  *  * | 0 0  0  0  0  0 0  0  2  2  0  0  0 0  0  0 0 | 0 0  0 0 1  2  1 0
... .xo ... ...&#x  |  0  2  1 |  0  0  1  0  2  0  0 |  *  *  *  *  *  *  *  *  * 60  *  *  *  * | 0 0  0  0  0  0 0  0  1  0  1  1  0 0  0  0 0 | 0 0  0 1 1  1  0 0
... ... ... .xx&#x  |  0  2  2 |  0  0  0  1  2  0  1 |  *  *  *  *  *  *  *  *  *  * 60  *  *  * | 0 0  0  0  0  0 0  0  0  1  0  1  1 0  0  0 0 | 0 0  0 1 0  1  1 0
..x3..o ... ...     |  0  0  3 |  0  0  0  0  0  3  0 |  *  *  *  *  *  *  *  *  *  *  * 20  *  * | 0 0  0  0  0  0 0  0  1  0  0  0  0 1  1  0 0 | 0 0  0 0 1  1  0 1
..x ... ... ..x     |  0  0  4 |  0  0  0  0  0  2  2 |  *  *  *  *  *  *  *  *  *  *  *  * 30  * | 0 0  0  0  0  0 0  0  0  1  0  0  0 0  1  1 0 | 0 0  0 0 0  1  1 1
... ... ..o3..x     |  0  0  3 |  0  0  0  0  0  0  3 |  *  *  *  *  *  *  *  *  *  *  *  *  * 20 | 0 0  0  0  0  0 0  0  0  0  0  0  1 0  0  1 1 | 0 0  0 1 0  0  1 1
--------------------+----------+----------------------+-------------------------------------------+-----------------------------------------------+-------------------
o..3x..3o.. ...     ♦  6  0  0 | 12  0  0  0  0  0  0 |  4  4  0  0  0  0  0  0  0  0  0  0  0  0 | 5 *  *  *  *  * *  *  *  *  *  *  * *  *  * * | 1 1  0 0 0  0  0 0
... x..3o..3o..     ♦  4  0  0 |  6  0  0  0  0  0  0 |  0  4  0  0  0  0  0  0  0  0  0  0  0  0 | * 5  *  *  *  * *  *  *  *  *  *  * *  *  * * | 1 0  0 1 0  0  0 0
oo.3xx. ... ...&#x  ♦  3  3  0 |  3  3  3  0  0  0  0 |  1  0  3  0  1  0  0  0  0  0  0  0  0  0 | * * 20  *  *  * *  *  *  *  *  *  * *  *  * * | 0 1  1 0 0  0  0 0
... xx.3oo. ...&#x  ♦  3  3  0 |  3  3  3  0  0  0  0 |  0  1  3  0  0  1  0  0  0  0  0  0  0  0 | * *  * 20  *  * *  *  *  *  *  *  * *  *  * * | 0 1  0 1 0  0  0 0
... xx. ... ox.&#x  ♦  2  4  0 |  1  4  2  2  0  0  0 |  0  0  2  2  0  0  1  0  0  0  0  0  0  0 | * *  *  * 30  * *  *  *  *  *  *  * *  *  * * | 0 0  1 1 0  0  0 0
... ... oo.3ox.&#x  ♦  1  3  0 |  0  3  0  3  0  0  0 |  0  0  0  3  0  0  0  1  0  0  0  0  0  0 | * *  *  *  * 10 *  *  *  *  *  *  * *  *  * * | 0 0  0 2 0  0  0 0
.o.3.x.3.o. ...     ♦  0  6  0 |  0  0 12  0  0  0  0 |  0  0  0  0  4  4  0  0  0  0  0  0  0  0 | * *  *  *  *  * 5  *  *  *  *  *  * *  *  * * | 0 1  0 0 1  0  0 0
.o.3.x. ... .x.     ♦  0  6  0 |  0  0  6  3  0  0  0 |  0  0  0  0  2  0  3  0  0  0  0  0  0  0 | * *  *  *  *  * * 10  *  *  *  *  * *  *  * * | 0 0  1 0 0  1  0 0
.ox3.xo ... ...&#x  ♦  0  3  3 |  0  0  3  0  6  3  0 |  0  0  0  0  1  0  0  0  3  3  0  1  0  0 | * *  *  *  *  * *  * 20  *  *  *  * *  *  * * | 0 0  0 0 1  1  0 0
.ox ... ... .xx&#x  ♦  0  2  4 |  0  0  0  1  4  2  2 |  0  0  0  0  0  0  0  0  2  0  2  0  1  0 | * *  *  *  *  * *  *  * 30  *  *  * *  *  * * | 0 0  0 0 0  1  1 0
... .xo3.oo ...&#x  ♦  0  3  1 |  0  0  3  0  3  0  0 |  0  0  0  0  0  1  0  0  0  3  0  0  0  0 | * *  *  *  *  * *  *  *  * 20  *  * *  *  * * | 0 0  0 1 1  0  0 0
... .xo ... .xx&#x  ♦  0  4  2 |  0  0  2  2  4  0  1 |  0  0  0  0  0  0  1  0  0  2  2  0  0  0 | * *  *  *  *  * *  *  *  *  * 30  * *  *  * * | 0 0  0 1 0  1  0 0
... ... .oo3.xx&#x  ♦  0  3  3 |  0  0  0  3  3  0  3 |  0  0  0  0  0  0  0  1  0  0  3  0  0  1 | * *  *  *  *  * *  *  *  *  *  * 20 *  *  * * | 0 0  0 1 0  0  1 0
..x3..o3..o ...     ♦  0  0  4 |  0  0  0  0  0  6  0 |  0  0  0  0  0  0  0  0  0  0  0  4  0  0 | * *  *  *  *  * *  *  *  *  *  *  * 5  *  * * | 0 0  0 0 1  0  0 1
..x3..o ... ..x     ♦  0  0  6 |  0  0  0  0  0  6  3 |  0  0  0  0  0  0  0  0  0  0  0  2  3  0 | * *  *  *  *  * *  *  *  *  *  *  * * 10  * * | 0 0  0 0 0  1  0 1
..x ... ..o3..x     ♦  0  0  6 |  0  0  0  0  0  3  6 |  0  0  0  0  0  0  0  0  0  0  0  0  3  2 | * *  *  *  *  * *  *  *  *  *  *  * *  * 10 * | 0 0  0 0 0  0  1 1
... ..o3..o3..x     ♦  0  0  4 |  0  0  0  0  0  0  6 |  0  0  0  0  0  0  0  0  0  0  0  0  0  4 | * *  *  *  *  * *  *  *  *  *  *  * *  *  * 5 | 0 0  0 1 0  0  0 1
--------------------+----------+----------------------+-------------------------------------------+-----------------------------------------------+-------------------
o..3x..3o..3o..     ♦ 10  0  0 | 30  0  0  0  0  0  0 | 10 20  0  0  0  0  0  0  0  0  0  0  0  0 | 5 5  0  0  0  0 0  0  0  0  0  0  0 0  0  0 0 | 1 *  * * *  *  * *
oo.3xx.3oo. ...&#x  ♦  6  6  0 | 12  6 12  0  0  0  0 |  4  4 12  0  4  4  0  0  0  0  0  0  0  0 | 1 0  4  4  0  0 1  0  0  0  0  0  0 0  0  0 0 | * 5  * * *  *  * *
oo.3xx. ... ox.&#x  ♦  3  6  0 |  3  6  6  3  0  0  0 |  1  0  6  3  2  0  3  0  0  0  0  0  0  0 | 0 0  2  0  3  0 0  1  0  0  0  0  0 0  0  0 0 | * * 10 * *  *  * *
... xxo3ooo3oxx&#xt ♦  4 12  4 |  6 12 12 12 12  0  6 |  0  4 12 12  0  4  6  4  0 12 12  0  0  4 | 0 1  0  4  6  4 0  0  0  0  4  6  4 0  0  0 1 | * *  * 5 *  *  * *
.ox3.xo3.oo ...&#x  ♦  0  6  4 |  0  0 12  0 12  6  0 |  0  0  0  0  4  4  0  0  6 12  0  4  0  0 | 0 0  0  0  0  0 1  0  4  0  4  0  0 1  0  0 0 | * *  * * 5  *  * *
.ox3.xo ... .xx&#x  ♦  0  6  6 |  0  0  6  3 12  6  3 |  0  0  0  0  2  0  3  0  6  6  6  2  3  0 | 0 0  0  0  0  0 0  1  2  3  0  3  0 0  1  0 0 | * *  * * * 10  * *
.ox ... .oo3.xx&#x  ♦  0  3  6 |  0  0  0  3  6  3  6 |  0  0  0  0  0  0  0  1  3  0  6  0  3  2 | 0 0  0  0  0  0 0  0  0  3  0  0  2 0  0  1 0 | * *  * * *  * 10 *
..x3..o3..o3..x     ♦  0  0 20 |  0  0  0  0  0 30 30 |  0  0  0  0  0  0  0  0  0  0  0 20 30 20 | 0 0  0  0  0  0 0  0  0  0  0  0  0 5 10 10 5 | * *  * * *  *  * 1

o(xo)(xo)o3x(ou)(xo)x x(xo)(ou)x3o(xo)(xo)o&#xt   → all heights = 
(triddip || (comp. of inv. thiddip large triangle) || (comp. of inv. thiddip large triangle, each wrt. the other subspace) || triddip)

...