Acronym	spid
Name	small prismatodecachoron, runcinated pentachoron
Cross sections	©
Circumradius	1
Vertex figure	©
Vertex layers	Layer Symmetry Subsymmetries   o3o3o3o o3o3o . o3o . o o . o3o . o3o3o 1 x3o3o3x x3o3o . tet first x3o . x trip first x . o3x trip first . o3o3x tet first 2a x3o3x . x3x . o o . x3x . x3o3x 2b o3o . u u . o3o 3 o3o3x . opposite tet o3x . x opposite trip x . x3o opposite trip . x3o3o opposite tet
Lace city in approx. ASCII-art	x3o o3o x3o x3x o3x o3o o3x
General of army	(is itself convex)
Colonel of regiment	(is itself locally convex – other uniform polychoral members: by cells: co oho tet trip piphid 5 0 5 10 duhd 0 5 10 0 spid 0 0 10 20   & others)
Confer	compounds: dopix   segmentochora: tet || co
External links

Incidence matrix according to Dynkin symbol

x3o3o3x

. . . . | 20 |  3  3 |  3  6  3 | 1  3  3 1
--------+----+-------+----------+----------
x . . . |  2 | 30  * |  2  2  0 | 1  2  1 0
. . . x |  2 |  * 30 |  0  2  2 | 0  1  2 1
--------+----+-------+----------+----------
x3o . . |  3 |  3  0 | 20  *  * | 1  1  0 0
x . . x |  4 |  2  2 |  * 30  * | 0  1  1 0
. . o3x |  3 |  0  3 |  *  * 20 | 0  0  1 1
--------+----+-------+----------+----------
x3o3o . ♦  4 |  6  0 |  4  0  0 | 5  *  * *
x3o . x ♦  6 |  6  3 |  2  3  0 | * 10  * *
x . o3x ♦  6 |  3  6 |  0  3  2 | *  * 10 *
. o3o3x ♦  4 |  0  6 |  0  0  4 | *  *  * 5

or
. . . .    | 20 |  6 |  6  6 |  2  6
-----------+----+----+-------+------
x . . .  & |  2 | 60 |  2  2 |  1  3
-----------+----+----+-------+------
x3o . .  & |  3 |  3 | 40  * |  1  1
x . . x    |  4 |  4 |  * 30 |  0  2
-----------+----+----+-------+------
x3o3o .  & ♦  4 |  6 |  4  0 | 10  *
x3o . x  & ♦  6 |  9 |  2  3 |  * 20

x3o3/2o3/2x

. .   .   . | 20 |  3  3 |  3  6  3 | 1  3  3 1
------------+----+-------+----------+----------
x .   .   . |  2 | 30  * |  2  2  0 | 1  2  1 0
. .   .   x |  2 |  * 30 |  0  2  2 | 0  1  2 1
------------+----+-------+----------+----------
x3o   .   . |  3 |  3  0 | 20  *  * | 1  1  0 0
x .   .   x |  4 |  2  2 |  * 30  * | 0  1  1 0
. .   o3/2x |  3 |  0  3 |  *  * 20 | 0  0  1 1
------------+----+-------+----------+----------
x3o3/2o   . ♦  4 |  6  0 |  4  0  0 | 5  *  * *
x3o   .   x ♦  6 |  6  3 |  2  3  0 | * 10  * *
x .   o3/2x ♦  6 |  3  6 |  0  3  2 | *  * 10 *
. o3/2o3/2x ♦  4 |  0  6 |  0  0  4 | *  *  * 5

x3/2o3o3/2x

.   . .   . | 20 |  3  3 |  3  6  3 | 1  3  3 1
------------+----+-------+----------+----------
x   . .   . |  2 | 30  * |  2  2  0 | 1  2  1 0
.   . .   x |  2 |  * 30 |  0  2  2 | 0  1  2 1
------------+----+-------+----------+----------
x3/2o .   . |  3 |  3  0 | 20  *  * | 1  1  0 0
x   . .   x |  4 |  2  2 |  * 30  * | 0  1  1 0
.   . o3/2x |  3 |  0  3 |  *  * 20 | 0  0  1 1
------------+----+-------+----------+----------
x3/2o3o   . ♦  4 |  6  0 |  4  0  0 | 5  *  * *
x3/2o .   x ♦  6 |  6  3 |  2  3  0 | * 10  * *
x   . o3/2x ♦  6 |  3  6 |  0  3  2 | *  * 10 *
.   o3o3/2x ♦  4 |  0  6 |  0  0  4 | *  *  * 5

xxo3ooo3oxx&#xt   → both heights = sqrt(5/8) = 0.790569
(tet || pseudo co || dual tet)

o..3o..3o..    | 4  * * | 3  3  0  0  0 0 | 3  6  3 0 0 0  0  0 0 | 1 3 3 1 0 0 0 0
.o.3.o.3.o.    | * 12 * | 0  1  2  2  1 0 | 0  2  2 1 2 1  2  2 0 | 0 1 2 1 1 2 1 0
..o3..o3..o    | *  * 4 | 0  0  0  0  3 3 | 0  0  0 0 0 0  3  6 3 | 0 0 0 0 1 3 3 1
---------------+--------+-----------------+-----------------------+----------------
x.. ... ...    | 2  0 0 | 6  *  *  *  * * | 2  2  0 0 0 0  0  0 0 | 1 2 1 0 0 0 0 0
oo.3oo.3oo.&#x | 1  1 0 | * 12  *  *  * * | 0  2  2 0 0 0  0  0 0 | 0 1 2 1 0 0 0 0
.x. ... ...    | 0  2 0 | *  * 12  *  * * | 0  1  0 1 1 0  1  0 0 | 0 1 1 0 1 1 0 0
... ... .x.    | 0  2 0 | *  *  * 12  * * | 0  0  1 0 1 1  0  1 0 | 0 0 1 1 0 1 1 0 
.oo3.oo3.oo&#x | 0  1 1 | *  *  *  * 12 * | 0  0  0 0 0 0  2  2 0 | 0 0 0 0 1 1 1 0
... ... ..x    | 0  0 2 | *  *  *  *  * 6 | 0  0  0 0 0 0  0  2 2 | 0 0 0 0 0 1 2 1
---------------+--------+-----------------+-----------------------+----------------
x..3o.. ...    | 3  0 0 | 3  0  0  0  0 0 | 4  *  * * * *  *  * * | 1 1 0 0 0 0 0 0
xx. ... ...&#x | 2  2 0 | 1  2  1  0  0 0 | * 12  * * * *  *  * * | 0 1 1 0 0 0 0 0
... ... ox.&#x | 1  2 0 | 0  2  0  1  0 0 | *  * 12 * * *  *  * * | 0 0 1 1 0 0 0 0
.x.3.o. ...    | 0  3 0 | 0  0  3  0  0 0 | *  *  * 4 * *  *  * * | 0 1 0 0 1 0 0 0
.x. ... .x.    | 0  4 0 | 0  0  2  2  0 0 | *  *  * * 6 *  *  * * | 0 0 1 0 0 1 0 0
... .o.3.x.    | 0  3 0 | 0  0  0  3  0 0 | *  *  * * * 4  *  * * | 0 0 0 1 0 0 1 0
.xo ... ...&#x | 0  2 1 | 0  0  1  0  2 0 | *  *  * * * * 12  * * | 0 0 0 0 1 1 0 0
... ... .xx&#x | 0  2 2 | 0  0  0  1  2 1 | *  *  * * * *  * 12 * | 0 0 0 0 0 1 1 0
... ..o3..x    | 0  0 3 | 0  0  0  0  0 3 | *  *  * * * *  *  * 4 | 0 0 0 0 0 0 1 1
---------------+--------+-----------------+-----------------------+----------------
x..3o..3o..    ♦ 4  0 0 | 6  0  0  0  0 0 | 4  0  0 0 0 0  0  0 0 | 1 * * * * * * *
xx.3oo. ...&#x ♦ 3  3 0 | 3  3  3  0  0 0 | 1  3  0 1 0 0  0  0 0 | * 4 * * * * * *
xx. ... ox.&#x ♦ 2  4 0 | 1  4  2  2  0 0 | 0  2  2 0 1 0  0  0 0 | * * 6 * * * * *
... oo.3ox.&#x ♦ 1  3 0 | 0  3  0  3  0 0 | 0  0  3 0 0 1  0  0 0 | * * * 4 * * * *
.xo3.oo ...&#x ♦ 0  3 1 | 0  0  3  0  3 0 | 0  0  0 1 0 0  3  0 0 | * * * * 4 * * *
.xo ... .xx&#x ♦ 0  4 2 | 0  0  2  2  4 1 | 0  0  0 0 1 0  2  2 0 | * * * * * 6 * *
... .oo3.xx&#x ♦ 0  3 3 | 0  0  0  3  3 3 | 0  0  0 0 0 1  0  3 1 | * * * * * * 4 *
..o3..o3..x    ♦ 0  0 4 | 0  0  0  0  0 6 | 0  0  0 0 0 0  0  0 4 | * * * * * * * 1

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