Acronym srip
Name small rhombated pentachoron,
cantellated pentachoron
 
    ©
(seen oct first   –                         seen co first)
Cross sections
 ©
Circumradius sqrt(7/5) = 1.183216
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o3o o3o3o . o3o . o o . o3o . o3o3o
1x3o3x3o x3o3x .
co first
x3o . o
{3} first
x . x3o
trip first
. o3x3o
oct first
2a x3x3o . x3x . x u . o3x . x3x3o
2b o . u3o
3a o3x3o .
opposite oct
o3x . u x . x3x . x3o3x
opposite co
3b u3o . o
4   x3o . x
opposite trip
o . x3o
opposite {3}
 
Lace city
in approx. ASCII-art
    x3o  o3x  		-- o3x3o (oct)
              
x3o  u3o  x3x 		-- x3x3o (tut)
              
 o3x  x3x  x3o		-- x3o3x (co)
   o o   x x   o o   
                     
                     
o x   x u   u x   x o
                     
                     
   x x  ou uo  x x   
General of army (is itself convex)
Colonel of regiment (is itself locally convex – other uniform polychoral members:
by cells: cho co hip oct oho trip tut
garpop 50100000
sirdop 50000105
pippindip 05105005
srip 05050100
pinnipdip 001055100
pirpop 001000105
rawvtip 0005505
)
Dihedral angles
  • at {3} between oct and trip:   arccos(-sqrt[3/8]) = 127.761244°
  • at {4} between co and trip:   arccos(-1/sqrt(6)) = 114.094843°
  • at {3} between co and oct:   arccos(-1/4) = 104.477512°
  • at {3} between co and co:   arccos(1/4) = 75.522488°
Dual m3o3m3o
Confer
Grünbaumian relatives:
2srip   2srip+20{6}+40{3}   2srip+20{6}+60{3}   2srip+20trip  
segmentochora:
oct || tut   co || tut   {3} || hip  
related CRFs:
diminished srip   bidiminished srip  
general polytopal classes:
bistratic lace towers  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

Note that srip can be thought of as the external blend of 1 pen + 5 raps + 10 trafs + 10 pens + 5 copies. This decomposition is described as the (also subdimensioanlly) degenerate segmentoteron xo3ox3oo3ox&#x.


Incidence matrix according to Dynkin symbol

x3o3x3o

. . . . | 30   2  4 |  1  4  2  2 | 2  2 1
--------+----+-------+-------------+-------
x . . . |  2 | 30  * |  1  2  0  0 | 2  1 0
. . x . |  2 |  * 60 |  0  1  1  1 | 1  1 1
--------+----+-------+-------------+-------
x3o . . |  3 |  3  0 | 10  *  *  * | 2  0 0
x . x . |  4 |  2  2 |  * 30  *  * | 1  1 0
. o3x . |  3 |  0  3 |  *  * 20  * | 1  0 1
. . x3o |  3 |  0  3 |  *  *  * 20 | 0  1 1
--------+----+-------+-------------+-------
x3o3x .  12 | 12 12 |  4  6  4  0 | 5  * *
x . x3o   6 |  3  6 |  0  3  0  2 | * 10 *
. o3x3o   6 |  0 12 |  0  0  4  4 | *  * 5

snubbed forms: β3o3x3o, x3o3β3o, β3o3β3o

x3o3x3/2o

. . .   . | 30   2  4 |  1  4  2  2 | 2  2 1
----------+----+-------+-------------+-------
x . .   . |  2 | 30  * |  1  2  0  0 | 2  1 0
. . x   . |  2 |  * 60 |  0  1  1  1 | 1  1 1
----------+----+-------+-------------+-------
x3o .   . |  3 |  3  0 | 10  *  *  * | 2  0 0
x . x   . |  4 |  2  2 |  * 30  *  * | 1  1 0
. o3x   . |  3 |  0  3 |  *  * 20  * | 1  0 1
. . x3/2o |  3 |  0  3 |  *  *  * 20 | 0  1 1
----------+----+-------+-------------+-------
x3o3x   .  12 | 12 12 |  4  6  4  0 | 5  * *
x . x3/2o   6 |  3  6 |  0  3  0  2 | * 10 *
. o3x3/2o   6 |  0 12 |  0  0  4  4 | *  * 5

x3/2o3/2x3o

.   .   . . | 30   2  4 |  1  4  2  2 | 2  2 1
------------+----+-------+-------------+-------
x   .   . . |  2 | 30  * |  1  2  0  0 | 2  1 0
.   .   x . |  2 |  * 60 |  0  1  1  1 | 1  1 1
------------+----+-------+-------------+-------
x3/2o   . . |  3 |  3  0 | 10  *  *  * | 2  0 0
x   .   x . |  4 |  2  2 |  * 30  *  * | 1  1 0
.   o3/2x . |  3 |  0  3 |  *  * 20  * | 1  0 1
.   .   x3o |  3 |  0  3 |  *  *  * 20 | 0  1 1
------------+----+-------+-------------+-------
x3/2o3/2x .  12 | 12 12 |  4  6  4  0 | 5  * *
x   .   x3o   6 |  3  6 |  0  3  0  2 | * 10 *
.   o3/2x3o   6 |  0 12 |  0  0  4  4 | *  * 5

x3/2o3/2x3/2o

.   .   .   . | 30   2  4 |  1  4  2  2 | 2  2 1
--------------+----+-------+-------------+-------
x   .   .   . |  2 | 30  * |  1  2  0  0 | 2  1 0
.   .   x   . |  2 |  * 60 |  0  1  1  1 | 1  1 1
--------------+----+-------+-------------+-------
x3/2o   .   . |  3 |  3  0 | 10  *  *  * | 2  0 0
x   .   x   . |  4 |  2  2 |  * 30  *  * | 1  1 0
.   o3/2x   . |  3 |  0  3 |  *  * 20  * | 1  0 1
.   .   x3/2o |  3 |  0  3 |  *  *  * 20 | 0  1 1
--------------+----+-------+-------------+-------
x3/2o3/2x   .  12 | 12 12 |  4  6  4  0 | 5  * *
x   .   x3/2o   6 |  3  6 |  0  3  0  2 | * 10 *
.   o3/2x3/2o   6 |  0 12 |  0  0  4  4 | *  * 5

oxx3xxo3oox&#xt   → both heights = sqrt(5/8) = 0.790569
(oct || pseudo tut || co)

o..3o..3o..     | 6  *  *   4  2 0  0  0  0  0 | 2 2 1  4 0  0  0  0 0 0 0 | 1 2 2 0 0 0
.o.3.o.3.o.     | * 12  *   0  1 1  2  2  0  0 | 0 0 1  2 1  2  2  1 0 0 0 | 0 2 1 1 1 0
..o3..o3..o     | *  * 12   0  0 0  0  2  2  2 | 0 0 0  0 0  2  1  2 1 2 1 | 0 1 0 2 1 1
----------------+---------+---------------------+---------------------------+------------
... x.. ...     | 2  0  0 | 12  * *  *  *  *  * | 1 1 0  1 0  0  0  0 0 0 0 | 1 1 1 0 0 0
oo.3oo.3oo.&#x  | 1  1  0 |  * 12 *  *  *  *  * | 0 0 1  2 0  0  0  0 0 0 0 | 0 2 1 0 0 0
.x. ... ...     | 0  2  0 |  *  * 6  *  *  *  * | 0 0 1  0 0  2  0  0 0 0 0 | 0 2 0 1 0 0
... .x. ...     | 0  2  0 |  *  * * 12  *  *  * | 0 0 0  1 1  0  1  0 0 0 0 | 0 1 1 0 1 0
.oo3.oo3.oo&#x  | 0  1  1 |  *  * *  * 24  *  * | 0 0 0  0 0  1  1  1 0 0 0 | 0 1 0 1 1 0
..x ... ...     | 0  0  2 |  *  * *  *  * 12  * | 0 0 0  0 0  1  0  0 1 1 0 | 0 1 0 1 0 1
... ... ..x     | 0  0  2 |  *  * *  *  *  * 12 | 0 0 0  0 0  0  0  1 0 1 1 | 0 0 0 1 1 1
----------------+---------+---------------------+---------------------------+------------
o..3x.. ...     | 3  0  0 |  3  0 0  0  0  0  0 | 4 * *  * *  *  *  * * * * | 1 1 0 0 0 0
... x..3o..     | 3  0  0 |  3  0 0  0  0  0  0 | * 4 *  * *  *  *  * * * * | 1 0 1 0 0 0
ox. ... ...&#x  | 1  2  0 |  0  2 1  0  0  0  0 | * * 6  * *  *  *  * * * * | 0 2 0 0 0 0
... xx. ...&#x  | 2  2  0 |  1  2 0  1  0  0  0 | * * * 12 *  *  *  * * * * | 0 1 1 0 0 0
... .x.3.o.     | 0  3  0 |  0  0 0  3  0  0  0 | * * *  * 4  *  *  * * * * | 0 0 1 0 1 0
.xx ... ...&#x  | 0  2  2 |  0  0 1  0  2  1  0 | * * *  * * 12  *  * * * * | 0 1 0 1 0 0
... .xo ...&#x  | 0  2  1 |  0  0 0  1  2  0  0 | * * *  * *  * 12  * * * * | 0 1 0 0 1 0
... ... .ox&#x  | 0  1  2 |  0  0 0  0  2  0  1 | * * *  * *  *  * 12 * * * | 0 0 0 1 1 0
..x3..o ...     | 0  0  3 |  0  0 0  0  0  3  0 | * * *  * *  *  *  * 4 * * | 0 1 0 0 0 1
..x ... ..x     | 0  0  4 |  0  0 0  0  0  2  2 | * * *  * *  *  *  * * 6 * | 0 0 0 1 0 1
... ..o3..x     | 0  0  3 |  0  0 0  0  0  0  3 | * * *  * *  *  *  * * * 4 | 0 0 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 | 1 * * * * *
oxx3xxo ...&#xt  3  6  3 |  3  6 3  3  6  3  0 | 1 0 3  3 0  3  3  0 1 0 0 | * 4 * * * *
... xx.3oo.&#x   3  3  0 |  3  3 0  3  0  0  0 | 0 1 0  3 1  0  0  0 0 0 0 | * * 4 * * *
.xx ... .ox&#x   0  2  4 |  0  0 1  0  4  2  2 | 0 0 0  0 0  2  0  2 0 1 0 | * * * 6 * *
... .xo3.ox&#x   0  3  3 |  0  0 0  3  6  0  3 | 0 0 0  0 1  0  3  3 0 0 1 | * * * * 4 *
..x3..o3..x      0  0 12 |  0  0 0  0  0 12 12 | 0 0 0  0 0  0  0  0 4 6 4 | * * * * * 1

x(uo)xo x(ou)xx3o(xo)xo&#xt   all 3 heights = sqrt(5/12) = 0.645497
(trip || compound of gyrated pseudo u x3o and (ungyrated) u-{3} || pseudo hip || {3})

o(..).. o(..)..3o(..)..     | 6 * *  * *  1 2  2 1 0  0  0 0 0 0  0 0 | 2 1 2 1 1  2 0 0 0 0 0 0 0 0 0 0 | 1 1 2 1 0 0 0
.(o.).. .(o.)..3.(o.)..     | * 6 *  * *  0 0  2 0 2  2  0 0 0 0  0 0 | 0 0 1 2 0  2 1 1 2 0 0 0 0 0 0 0 | 0 1 1 2 1 0 0
.(.o).. .(.o)..3.(.o)..     | * * 3  * *  0 0  0 2 0  0  4 0 0 0  0 0 | 0 0 0 0 1  4 0 0 0 2 2 0 0 0 0 0 | 0 0 2 2 0 1 0
.(..)o. .(..)o.3.(..)o.     | * * * 12 *  0 0  0 0 0  1  1 1 1 1  1 0 | 0 0 0 0 0  1 0 1 1 1 1 1 1 1 1 0 | 0 0 1 1 1 1 1
.(..).o .(..).o3.(..).o     | * * *  * 3  0 0  0 0 0  0  0 0 0 0  4 2 | 0 0 0 0 0  0 0 0 0 0 0 0 2 4 2 1 | 0 0 0 0 2 1 2
----------------------------+------------+-----------------------------+----------------------------------+--------------
x(..).. .(..).. .(..)..     | 2 0 0  0 0 | 3 *  * * *  *  * * * *  * * | 2 0 0 0 1  0 0 0 0 0 0 0 0 0 0 0 | 1 0 2 0 0 0 0
.(..).. x(..).. .(..)..     | 2 0 0  0 0 | * 6  * * *  *  * * * *  * * | 1 1 1 0 0  0 0 0 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0 0
o(o.).. o(o.)..3o(o.)..&#x  | 1 1 0  0 0 | * * 12 * *  *  * * * *  * * | 0 0 1 1 0  1 0 0 0 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0
o(.o).. o(.o)..3o(.o)..&#x  | 1 0 1  0 0 | * *  * 6 *  *  * * * *  * * | 0 0 0 0 1  2 0 0 0 0 0 0 0 0 0 0 | 0 0 2 1 0 0 0
.(..).. .(..).. .(x.)..     | 0 2 0  0 0 | * *  * * 6  *  * * * *  * * | 0 0 0 1 0  0 1 0 1 0 0 0 0 0 0 0 | 0 1 0 1 1 0 0
.(o.)o. .(o.)o.3.(o.)o.&#x  | 0 1 0  1 0 | * *  * * * 12  * * * *  * * | 0 0 0 0 0  1 0 1 1 0 0 0 0 0 0 0 | 0 0 1 1 1 0 0
.(.o)o. .(.o)o.3.(.o)o.&#x  | 0 0 1  1 0 | * *  * * *  * 12 * * *  * * | 0 0 0 0 0  1 0 0 0 1 1 0 0 0 0 0 | 0 0 1 1 0 1 0
.(..)x. .(..).. .(..)..     | 0 0 0  2 0 | * *  * * *  *  * 6 * *  * * | 0 0 0 0 0  0 0 0 0 1 0 1 1 0 0 0 | 0 0 1 0 0 1 1
.(..).. .(..)x. .(..)..     | 0 0 0  2 0 | * *  * * *  *  * * 6 *  * * | 0 0 0 0 0  0 0 1 0 0 0 1 0 1 0 0 | 0 0 1 0 1 0 1
.(..).. .(..).. .(..)x.     | 0 0 0  2 0 | * *  * * *  *  * * * 6  * * | 0 0 0 0 0  0 0 0 1 0 1 0 0 0 1 0 | 0 0 0 1 1 1 0
.(..)oo .(..)oo3.(..)oo&#x  | 0 0 0  1 1 | * *  * * *  *  * * * * 12 * | 0 0 0 0 0  0 0 0 0 0 0 0 1 1 1 0 | 0 0 0 0 1 1 1
.(..).. .(..).x .(..)..     | 0 0 0  0 2 | * *  * * *  *  * * * *  * 3 | 0 0 0 0 0  0 0 0 0 0 0 0 0 2 0 1 | 0 0 0 0 2 0 1
----------------------------+------------+-----------------------------+----------------------------------+--------------
x(..).. x(..).. .(..)..     | 4 0 0  0 0 | 2 2  0 0 0  0  0 0 0 0  0 0 | 3 * * * *  * * * * * * * * * * * | 1 0 1 0 0 0 0
.(..).. x(..)..3o(..)..     | 3 0 0  0 0 | 0 3  0 0 0  0  0 0 0 0  0 0 | * 2 * * *  * * * * * * * * * * * | 1 1 0 0 0 0 0
.(..).. x(o.).. .(..)..&#x  | 2 1 0  0 0 | 0 1  2 0 0  0  0 0 0 0  0 0 | * * 6 * *  * * * * * * * * * * * | 0 1 1 0 0 0 0
.(..).. .(..).. o(x.)..&#x  | 1 2 0  0 0 | 0 0  2 0 1  0  0 0 0 0  0 0 | * * * 6 *  * * * * * * * * * * * | 0 1 0 1 0 0 0
x(.o).. .(..).. .(..)..&#x  | 2 0 1  0 0 | 1 0  0 2 0  0  0 0 0 0  0 0 | * * * * 3  * * * * * * * * * * * | 0 0 2 0 0 0 0
o(oo)o. o(oo)o.3o(oo)o.&#xr | 1 1 1  1 0 | 0 0  1 1 0  1  1 0 0 0  0 0 | * * * * * 12 * * * * * * * * * * | 0 0 1 1 0 0 0
.(..).. .(o.)..3.(x.)..     | 0 3 0  0 0 | 0 0  0 0 3  0  0 0 0 0  0 0 | * * * * *  * 2 * * * * * * * * * | 0 1 0 0 1 0 0
.(..).. .(o.)x. .(..)..&#x  | 0 1 0  2 0 | 0 0  0 0 0  2  0 0 1 0  0 0 | * * * * *  * * 6 * * * * * * * * | 0 0 1 0 1 0 0
.(..).. .(..).. .(x.)x.&#x  | 0 2 0  2 0 | 0 0  0 0 1  2  0 0 0 1  0 0 | * * * * *  * * * 6 * * * * * * * | 0 0 0 1 1 0 0
.(.o)x. .(..).. .(..)..&#x  | 0 0 1  2 0 | 0 0  0 0 0  0  2 1 0 0  0 0 | * * * * *  * * * * 6 * * * * * * | 0 0 1 0 0 1 0
.(..).. .(..).. .(.o)x.&#x  | 0 0 1  2 0 | 0 0  0 0 0  0  2 0 0 1  0 0 | * * * * *  * * * * * 6 * * * * * | 0 0 0 1 0 1 0
.(..)x. .(..)x. .(..)..     | 0 0 0  4 0 | 0 0  0 0 0  0  0 2 2 0  0 0 | * * * * *  * * * * * * 3 * * * * | 0 0 1 0 0 0 1
.(..)xo .(..).. .(..)..&#x  | 0 0 0  2 1 | 0 0  0 0 0  0  0 1 0 0  2 0 | * * * * *  * * * * * * * 6 * * * | 0 0 0 0 0 1 1
.(..).. .(..)xx .(..)..&#x  | 0 0 0  2 2 | 0 0  0 0 0  0  0 0 1 0  2 1 | * * * * *  * * * * * * * * 6 * * | 0 0 0 0 1 0 1
.(..).. .(..).. .(..)xo&#x  | 0 0 0  2 1 | 0 0  0 0 0  0  0 0 0 1  2 0 | * * * * *  * * * * * * * * * 6 * | 0 0 0 0 1 1 0
.(..).. .(..).x3.(..).o     | 0 0 0  0 3 | 0 0  0 0 0  0  0 0 0 0  0 3 | * * * * *  * * * * * * * * * * 1 | 0 0 0 0 2 0 0
----------------------------+------------+-----------------------------+----------------------------------+--------------
x(..).. x(..)..3o(..)..      6 0 0  0 0 | 3 6  0 0 0  0  0 0 0 0  0 0 | 3 2 0 0 0  0 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * *
.(..).. x(o.)..3o(x.)..&#x   3 3 0  0 0 | 0 3  6 0 3  0  0 0 0 0  0 0 | 0 1 3 3 0  0 1 0 0 0 0 0 0 0 0 0 | * 2 * * * * *
x(uo)x. x(ou)x. .(..)..&#xt  4 2 2  4 0 | 2 2  4 4 0  4  4 2 2 0  0 0 | 1 0 2 0 2  4 0 2 0 2 0 1 0 0 0 0 | * * 3 * * * *
.(..).. .(..).. o(xo)x.&#xr  1 2 1  2 0 | 0 0  2 1 1  2  2 0 0 1  0 0 | 0 0 0 1 0  2 0 0 1 0 1 0 0 0 0 0 | * * * 6 * * *
.(..).. .(o.)xx3.(x.)xo&#xt  0 3 0  6 3 | 0 0  0 0 3  6  0 0 3 3  6 3 | 0 0 0 0 0  0 1 3 3 0 0 0 0 3 3 1 | * * * * 2 * *
.(.o)xo .(..).. .(.o)xo&#xt  0 0 1  4 1 | 0 0  0 0 0  0  4 2 0 2  4 0 | 0 0 0 0 0  0 0 0 0 2 2 0 2 0 2 0 | * * * * * 3 *
.(..)xo .(..)xx .(..)..&#x   0 0 0  4 2 | 0 0  0 0 0  0  0 2 2 0  4 1 | 0 0 0 0 0  0 0 0 0 0 0 1 2 2 0 0 | * * * * * * 3

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