sirn

Acronym

sirn

Name

small rhombated penteract,
cantellated penteract

Circumradius

[3+sqrt(2)]/2 = 2.207107

Inradius
wrt. rap

sqrt[(43+30 sqrt(2))/20] = 2.066717

Inradius
wrt. tepe

sqrt[(17+12 sqrt(2))/8] = 2.060660

Inradius
wrt. srit

(1+sqrt(2))/2 = 1.207107

Vertex figure

©

Lace city
in approx. ASCII-art

©	x3o4x o3x4x o3x4x x3o4x -- o3x3o4x (srit) o3x4x o3o4w o3o4w o3x4x -- o3o3x4x (tat) o3x4x o3o4w o3o4w o3x4x -- o3o3x4x (tat) x3o4x o3x4x o3x4x x3o4x -- o3x3o4x (srit)

Coordinates

((1+sqrt(2))/2, (1+sqrt(2))/2, (1+sqrt(2))/2, 1/2, 1/2) & all permutations, all changes of sign

Volume

[1205+843 sqrt(2)]/30 = 79.906068

Surface

[450+340 sqrt(2)+11 sqrt(5)]/3 = 318.476453

General of army

(is itself convex)

Colonel of regiment

(is itself locally convex – other uniform polyteral members:

by cells:	rap	rawvatoth	srit	tat	tepe
rawn	32	10	0	10	0
sirn	32	0	10	0	80

& others)

Dihedral angles
(at margins)

at tet between rap and tepe: arccos[-2/sqrt(5)] = 153.434949°
at trip between srit and tepe: 120°
at oct between rap and srit: arccos(-1/sqrt(5)) = 116.565051°
at sirco between srit and srit: 90°

Face vector

320, 1280, 1520, 680, 122

Confer

related segmentotera:: sircoa ticcup sritatat tattip
variations:: rerin
general polytopal classes:: Wythoffian polytera partial Stott expansions
analogs:: rhombated hypercube rbC_n

External
links

As abstract polytope sirn is isomorphic to quarn, thereby replacing sirco by querco and srit by qrit.

Incidence matrix according to Dynkin symbol

o3o3x3o4x

. . . . . | 320 |   6   2 |   6   3   6  1 |   2   3   6  3 |  1  2  3
----------+-----+---------+----------------+----------------+---------
. . x . . |   2 | 960   * |   2   1   1  0 |   1   2   2  1 |  1  1  2
. . . . x |   2 |   * 320 |   0   0   3  1 |   0   0   3  3 |  0  1  3
----------+-----+---------+----------------+----------------+---------
. o3x . . |   3 |   3   0 | 640   *   *  * |   1   1   1  0 |  1  1  1
. . x3o . |   3 |   3   0 |   * 320   *  * |   0   2   0  1 |  1  0  2
. . x . x |   4 |   2   2 |   *   * 480  * |   0   0   2  1 |  0  1  2
. . . o4x |   4 |   0   4 |   *   *   * 80 |   0   0   0  3 |  0  0  3
----------+-----+---------+----------------+----------------+---------
o3o3x . . ♦   4 |   6   0 |   4   0   0  0 | 160   *   *  * |  1  1  0
. o3x3o . ♦   6 |  12   0 |   4   4   0  0 |   * 160   *  * |  1  0  1
. o3x . x ♦   6 |   6   3 |   2   0   3  0 |   *   * 320  * |  0  1  1
. . x3o4x ♦  24 |  24  24 |   0   8  12  6 |   *   *   * 40 |  0  0  2
----------+-----+---------+----------------+----------------+---------
o3o3x3o . ♦  10 |  30   0 |  20  10   0  0 |   5   5   0  0 | 32  *  *
o3o3x . x ♦   8 |  12   4 |   8   0   6  0 |   2   0   4  0 |  * 80  *
. o3x3o4x ♦  96 | 192  96 |  64  64  96 24 |   0  16  32  8 |  *  * 10

snubbed forms: o3o3x3o4s

oooo3xoox3oxxo4xxxx&#xt   → outer heights = 1/sqrt(2) = 0.707107
                            inner height = 1
(srit || pseudo tat || pseudo tat || srit)

o...3o...3o...4o...     & | 192   * |   4   2   2   0  0  0 |   2   2   4  1   4   1   2   0  0  0 |  1  2  2   2   2   4  1  0  0 | 1  1  2 2  0
.o..3.o..3.o..4.o..     & |   * 128 |   0   0   3   3  1  1 |   0   0   0  0   3   3   3   3  3  1 |  0  0  0   1   3   3  3  1  3 | 0  1  1 3  1
--------------------------+---------+-----------------------+--------------------------------------+-------------------------------+-------------
.... x... .... ....     & |   2   0 | 384   *   *   *  *  * |   1   1   1  0   1   0   0   0  0  0 |  1  1  1   1   1   1  0  0  0 | 1  1  1 1  0
.... .... .... x...     & |   2   0 |   * 192   *   *  *  * |   0   0   2  1   0   0   1   0  0  0 |  0  1  2   0   0   2  1  0  0 | 1  0  1 2  0
oo..3oo..3oo..4oo..&#x  & |   1   1 |   *   * 384   *  *  * |   0   0   0  0   2   1   1   0  0  0 |  0  0  0   1   2   2  1  0  0 | 0  1  1 2  0
.... .... .x.. ....     & |   0   2 |   *   *   * 192  *  * |   0   0   0  0   0   1   0   2  1  0 |  0  0  0   0   2   0  1  1  2 | 0  1  0 2  1
.... .... .... .x..     & |   0   2 |   *   *   *   * 64  * |   0   0   0  0   0   0   3   0  0  1 |  0  0  0   0   0   3  3  0  0 | 0  0  1 3  0
.oo.3.oo.3.oo.4.oo.&#x    |   0   2 |   *   *   *   *  * 64 |   0   0   0  0   0   0   0   0  3  1 |  0  0  0   0   0   0  3  0  3 | 0  0  0 3  1
--------------------------+---------+-----------------------+--------------------------------------+-------------------------------+-------------
o...3x... .... ....     & |   3   0 |   3   0   0   0  0  0 | 128   *   *  *   *   *   *   *  *  * |  1  1  0   1   0   0  0  0  0 | 1  1  1 0  0
.... x...3o... ....     & |   3   0 |   3   0   0   0  0  0 |   * 128   *  *   *   *   *   *  *  * |  1  0  1   0   1   0  0  0  0 | 1  1  0 1  0
.... x... .... x...     & |   4   0 |   2   2   0   0  0  0 |   *   * 192  *   *   *   *   *  *  * |  0  1  1   0   0   1  0  0  0 | 1  0  1 1  0
.... .... o...4x...     & |   4   0 |   0   4   0   0  0  0 |   *   *   * 48   *   *   *   *  *  * |  0  0  2   0   0   0  1  0  0 | 1  0  0 2  0
.... xo.. .... ....&#x  & |   2   1 |   1   0   2   0  0  0 |   *   *   *  * 384   *   *   *  *  * |  0  0  0   1   1   1  0  0  0 | 0  1  1 1  0
.... .... ox.. ....&#x  & |   1   2 |   0   0   2   1  0  0 |   *   *   *  *   * 192   *   *  *  * |  0  0  0   0   2   0  1  0  0 | 0  1  0 2  0
.... .... .... xx..&#x  & |   2   2 |   0   1   2   0  1  0 |   *   *   *  *   *   * 192   *  *  * |  0  0  0   0   0   2  1  0  0 | 0  0  1 2  0
.... .o..3.x.. ....     & |   0   3 |   0   0   0   3  0  0 |   *   *   *  *   *   *   * 128  *  * |  0  0  0   0   1   0  0  1  1 | 0  1  0 1  1
.... .... .xx. ....&#x    |   0   4 |   0   0   0   2  0  2 |   *   *   *  *   *   *   *   * 96  * |  0  0  0   0   0   0  1  0  2 | 0  0  0 2  1
.... .... .... .xx.&#x    |   0   4 |   0   0   0   0  2  2 |   *   *   *  *   *   *   *   *  * 32 |  0  0  0   0   0   0  3  0  0 | 0  0  0 3  0
--------------------------+---------+-----------------------+--------------------------------------+-------------------------------+-------------
o...3x...3o... ....     & ♦   6   0 |  12   0   0   0  0  0 |   4   4   0  0   0   0   0   0  0  0 | 32  *  *   *   *   *  *  *  * | 1  1  0 0  0
o...3x... .... x...     & ♦   6   0 |   6   3   0   0  0  0 |   2   0   3  0   0   0   0   0  0  0 |  * 64  *   *   *   *  *  *  * | 1  0  1 0  0
.... x...3o...4x...     & ♦  24   0 |  24  24   0   0  0  0 |   0   8  12  6   0   0   0   0  0  0 |  *  * 16   *   *   *  *  *  * | 1  0  0 1  0
oo..3xo.. .... ....&#x  & ♦   3   1 |   3   0   3   0  0  0 |   1   0   0  0   3   0   0   0  0  0 |  *  *  * 128   *   *  *  *  * | 0  1  1 0  0
.... xo..3ox.. ....&#x  & ♦   3   3 |   3   0   6   3  0  0 |   0   1   0  0   3   3   0   1  0  0 |  *  *  *   * 128   *  *  *  * | 0  1  0 1  0
.... xo.. .... xx..&#x  & ♦   4   2 |   2   2   4   0  1  0 |   0   0   1  0   2   0   2   0  0  0 |  *  *  *   *   * 192  *  *  * | 0  0  1 1  0
.... .... oxxo4xxxx&#xt   ♦   8  16 |   0   8  16   8  8  8 |   0   0   0  2   0   8   8   0  4  4 |  *  *  *   *   *   * 24  *  * | 0  0  0 2  0
.o..3.o..3.x.. ....     & ♦   0   4 |   0   0   0   6  0  0 |   0   0   0  0   0   0   0   4  0  0 |  *  *  *   *   *   *  * 32  * | 0  1  0 0  1
.... .oo.3.xx. ....&#x    ♦   0   6 |   0   0   0   6  0  3 |   0   0   0  0   0   0   0   2  3  0 |  *  *  *   *   *   *  *  * 64 | 0  0  0 1  1
--------------------------+---------+-----------------------+--------------------------------------+-------------------------------+-------------
o...3x...3o...4x...     & ♦  96   0 | 192  96   0   0  0  0 |  64  64  96 24   0   0   0   0  0  0 | 16 32  8   0   0   0  0  0  0 | 2  *  * *  *
oo..3xo..3ox.. ....&#x  & ♦   6   4 |  12   0  12   6  0  0 |   4   4   0  0  12   6   0   4  0  0 |  1  0  0   4   4   0  0  1  0 | * 32  * *  *
oo..3xo.. .... xx..&#x  & ♦   6   2 |   6   3   6   0  1  0 |   2   0   3  0   6   0   3   0  0  0 |  0  1  0   2   0   3  0  0  0 | *  * 64 *  *
.... xoox3oxxo4xxxx&#xt   ♦  48  48 |  48  48  96  48 24 24 |   0  16  24 12  48  48  48  16 24 12 |  0  0  2   0  16  24  6  0  8 | *  *  * 8  *
.oo.3.oo.3.xx. ....&#x    ♦   0   8 |   0   0   0  12  0  4 |   0   0   0  0   0   0   0   8  6  0 |  0  0  0   0   0   0  0  2  4 | *  *  * * 16

oxo4wxx xoo3oxo4xxw&#zxt   → height = 0
(tegum sum of (w-{4},sirco)-duoprism and ({8},tic)-duoprism and ({4},w-cube)-duoprism)

o..4o.. o..3o..4o..      | 96   *  * |  2  2   4  0  0   0  0   0  0 |  1  2  1   2   4   2   4  0  0  0  0  0  0   0 0 | 1  2  1  2  2  2  4  0  0  0  0 | 1  1  2 2  0
.o.4.o. .o.3.o.4.o.      |  * 192  * |  0  0   2  1  1   2  1   1  0 |  0  0  0   2   1   2   2  1  2  1  1  1  1   2 0 | 0  1  2  2  2  1  1  1  1  2  1 | 2  1  1 1  1
..o4..o ..o3..o4..o      |  *   * 32 |  0  0   0  0  0   0  0   6  2 |  0  0  0   0   0   0   0  0  0  0  0  3  6   6 1 | 0  0  3  0  0  0  0  0  3  6  2 | 3  1  0 0  2
-------------------------+-----------+-------------------------------+--------------------------------------------------+---------------------------------+-------------
... ... x.. ... ...      |  2   0  0 | 96  *   *  *  *   *  *   *  * |  1  1  0   0   2   0   0  0  0  0  0  0  0   0 0 | 1  1  0  0  0  2  2  0  0  0  0 | 0  1  1 2  0
... ... ... ... x..      |  2   0  0 |  * 96   *  *  *   *  *   *  * |  0  1  1   0   0   0   2  0  0  0  0  0  0   0 0 | 1  0  0  1  2  0  2  0  0  0  0 | 1  0  1 2  0
oo.4oo. oo.3oo.4oo.&#x   |  1   1  0 |  *  * 384  *  *   *  *   *  * |  0  0  0   1   1   1   1  0  0  0  0  0  0   0 0 | 0  1  1  1  1  1  1  0  0  0  0 | 1  1  1 1  0
.x. ... ... ... ...      |  0   2  0 |  *  *   * 96  *   *  *   *  * |  0  0  0   2   0   0   0  1  0  0  0  1  0   0 0 | 0  1  2  2  0  0  0  0  1  0  0 | 2  1  1 0  0
... .x. ... ... ...      |  0   2  0 |  *  *   *  * 96   *  *   *  * |  0  0  0   0   0   0   0  0  2  1  0  0  1   0 0 | 0  0  0  0  2  0  0  1  1  2  0 | 2  0  0 1  1
... ... ... .x. ...      |  0   2  0 |  *  *   *  *  * 192  *   *  * |  0  0  0   0   0   1   0  0  1  0  1  0  0   1 0 | 0  0  1  0  1  1  0  1  0  1  1 | 1  1  0 1  1
... ... ... ... .x.      |  0   2  0 |  *  *   *  *  *   * 96   *  * |  0  0  0   0   0   0   2  1  0  1  0  0  0   0 0 | 0  0  0  2  2  0  1  0  1  0  0 | 2  0  1 1  0
.oo4.oo .oo3.oo4.oo&#x   |  0   1  1 |  *  *   *  *  *   *  * 192  * |  0  0  0   0   0   0   0  0  0  0  0  1  1   2 0 | 0  0  2  0  0  0  0  0  1  2  1 | 2  1  0 0  1
... ..x ... ... ...      |  0   0  2 |  *  *   *  *  *   *  *   * 32 |  0  0  0   0   0   0   0  0  0  0  0  0  3   0 1 | 0  0  0  0  0  0  0  0  3  3  0 | 3  0  0 0  1
-------------------------+-----------+-------------------------------+--------------------------------------------------+---------------------------------+-------------
... ... x..3o.. ...      |  3   0  0 |  3  0   0  0  0   0  0   0  0 | 32  *  *   *   *   *   *  *  *  *  *  *  *   * * | 1  0  0  0  0  2  0  0  0  0  0 | 0  1  0 2  0
... ... x.. ... x..      |  4   0  0 |  2  2   0  0  0   0  0   0  0 |  * 48  *   *   *   *   *  *  *  *  *  *  *   * * | 1  0  0  0  0  0  2  0  0  0  0 | 0  0  1 2  0
... ... ... o..4x..      |  4   0  0 |  0  4   0  0  0   0  0   0  0 |  *  * 24   *   *   *   *  *  *  *  *  *  *   * * | 1  0  0  0  2  0  0  0  0  0  0 | 1  0  0 2  0
ox. ... ... ... ...&#x   |  1   2  0 |  0  0   2  1  0   0  0   0  0 |  *  *  * 192   *   *   *  *  *  *  *  *  *   * * | 0  1  1  1  0  0  0  0  0  0  0 | 1  1  1 0  0
... ... xo. ... ...&#x   |  2   1  0 |  1  0   2  0  0   0  0   0  0 |  *  *  *   * 192   *   *  *  *  *  *  *  *   * * | 0  1  0  0  0  1  1  0  0  0  0 | 0  1  1 1  0
... ... ... ox. ...&#x   |  1   2  0 |  0  0   2  0  0   1  0   0  0 |  *  *  *   *   * 192   *  *  *  *  *  *  *   * * | 0  0  1  0  1  1  0  0  0  0  0 | 1  1  0 1  0
... ... ... ... xx.&#x   |  2   2  0 |  0  1   2  0  0   0  1   0  0 |  *  *  *   *   *   * 192  *  *  *  *  *  *   * * | 0  0  0  1  1  0  1  0  0  0  0 | 1  0  1 1  0
.x. ... ... ... .x.      |  0   4  0 |  0  0   0  2  0   0  2   0  0 |  *  *  *   *   *   *   * 48  *  *  *  *  *   * * | 0  0  0  2  0  0  0  0  1  0  0 | 2  0  1 0  0
... .x. ... .x. ...      |  0   4  0 |  0  0   0  0  2   2  0   0  0 |  *  *  *   *   *   *   *  * 96  *  *  *  *   * * | 0  0  0  0  1  0  0  1  0  1  0 | 1  0  0 1  1
... .x. ... ... .x.      |  0   4  0 |  0  0   0  0  2   0  2   0  0 |  *  *  *   *   *   *   *  *  * 48  *  *  *   * * | 0  0  0  0  2  0  0  0  1  0  0 | 2  0  0 1  0
... ... .o.3.x. ...      |  0   3  0 |  0  0   0  0  0   3  0   0  0 |  *  *  *   *   *   *   *  *  *  * 64  *  *   * * | 0  0  0  0  0  1  0  1  0  0  1 | 0  1  0 1  1
.xo ... ... ... ...&#x   |  0   2  1 |  0  0   0  1  0   0  0   2  0 |  *  *  *   *   *   *   *  *  *  *  * 96  *   * * | 0  0  2  0  0  0  0  0  1  0  0 | 2  1  0 0  0
... .xx ... ... ...&#x   |  0   2  2 |  0  0   0  0  1   0  0   2  1 |  *  *  *   *   *   *   *  *  *  *  *  * 96   * * | 0  0  0  0  0  0  0  0  1  2  0 | 2  0  0 0  1
... ... ... .xo ...&#x   |  0   2  1 |  0  0   0  0  0   1  0   2  0 |  *  *  *   *   *   *   *  *  *  *  *  *  * 192 * | 0  0  1  0  0  0  0  0  0  1  1 | 1  1  0 0  1
..o4..x ... ... ...      |  0   0  4 |  0  0   0  0  0   0  0   0  4 |  *  *  *   *   *   *   *  *  *  *  *  *  *   * 8 | 0  0  0  0  0  0  0  0  3  0  0 | 3  0  0 0  0
-------------------------+-----------+-------------------------------+--------------------------------------------------+---------------------------------+-------------
... ... x..3o..4x..      ♦ 24   0  0 | 24 24   0  0  0   0  0   0  0 |  8 12  6   0   0   0   0  0  0  0  0  0  0   0 0 | 4  *  *  *  *  *  *  *  *  *  * | 0  0  0 2  0
ox. ... xo. ... ...&#x   ♦  2   2  0 |  1  0   4  1  0   0  0   0  0 |  0  0  0   2   2   0   0  0  0  0  0  0  0   0 0 | * 96  *  *  *  *  *  *  *  *  * | 0  1  1 0  0
oxo ... ... oxo ...&#xt  ♦  1   4  1 |  0  0   4  2  0   2  0   4  0 |  0  0  0   2   0   2   0  0  0  0  0  2  0   2 0 | *  * 96  *  *  *  *  *  *  *  * | 1  1  0 0  0
ox. ... ... ... xx.&#x   ♦  2   4  0 |  0  1   4  2  0   0  2   0  0 |  0  0  0   2   0   0   2  1  0  0  0  0  0   0 0 | *  *  * 96  *  *  *  *  *  *  * | 1  0  1 0  0
... wx. ... ox.4xx.&#zx  ♦  8  16  0 |  0  8  16  0  8   8  8   0  0 |  0  0  2   0   0   8   8  0  4  4  0  0  0   0 0 | *  *  *  * 24  *  *  *  *  *  * | 1  0  0 1  0
... ... xo.3ox. ...&#x   ♦  3   3  0 |  3  0   6  0  0   3  0   0  0 |  1  0  0   0   3   3   0  0  0  0  1  0  0   0 0 | *  *  *  *  * 64  *  *  *  *  * | 0  1  0 1  0
... ... xo. ... xx.&#x   ♦  4   2  0 |  2  2   4  0  0   0  1   0  0 |  0  1  0   0   2   0   2  0  0  0  0  0  0   0 0 | *  *  *  *  *  * 96  *  *  *  * | 0  0  1 1  0
... .x. .o.3.x. ...      ♦  0   6  0 |  0  0   0  0  3   6  0   0  0 |  0  0  0   0   0   0   0  0  3  0  2  0  0   0 0 | *  *  *  *  *  *  * 32  *  *  * | 0  0  0 1  1
.xo4.xx ... ... .xw&#zx  ♦  0  16  8 |  0  0   0  8  8   0  8  16  8 |  0  0  0   0   0   0   0  4  0  4  0  8  8   0 2 | *  *  *  *  *  *  *  * 12  *  * | 2  0  0 0  0
... .xx ... .xo ...&#x   ♦  0   4  2 |  0  0   0  0  2   2  0   4  1 |  0  0  0   0   0   0   0  0  1  0  0  0  2   2 0 | *  *  *  *  *  *  *  *  * 96  * | 1  0  0 0  1
... ... .oo3.xo ...&#x   ♦  0   3  1 |  0  0   0  0  0   3  0   3  0 |  0  0  0   0   0   0   0  0  0  0  1  0  0   3 0 | *  *  *  *  *  *  *  *  *  * 64 | 0  1  0 0  1
-------------------------+-----------+-------------------------------+--------------------------------------------------+---------------------------------+-------------
oxo4wxx ... oxo4xxw&#zxt ♦ 16  64 16 |  0 16  64 32 32  32 32  64 16 |  0  0  4  32   0  32  32 16 16 16  0 32 32  32 4 | 0  0 16 16  4  0  0  0  4 16  0 | 6  *  * *  *
oxo ... xoo3oxo ...&#xt  ♦  3   6  1 |  3  0  12  3  0   6  0   6  0 |  1  0  0   6   6   6   0  0  0  0  2  3  0   6 0 | 0  3  3  0  0  2  0  0  0  0  2 | * 32  * *  *
ox. ... xo. ... xx.&#x   ♦  4   4  0 |  2  2   8  2  0   0  2   0  0 |  0  1  0   4   4   0   4  1  0  0  0  0  0   0 0 | 0  2  0  2  0  0  2  0  0  0  0 | *  * 48 *  *
... wx. xo.3ox.4xx.&#zx  ♦ 48  48  0 | 48 48  96  0 24  48 24   0  0 | 16 24 12   0  48  48  48  0 24 12 16  0  0   0 0 | 2  0  0  0  6 16 24  8  0  0  0 | *  *  * 4  *
... .xx .oo3.xo ...&#x   ♦  0   6  2 |  0  0   0  0  3   6  0   6  1 |  0  0  0   0   0   0   0  0  3  0  2  0  3   6 0 | 0  0  0  0  0  0  0  1  0  3  2 | *  *  * * 32

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