Acronym spid
Name small prismatodecachoron,
runcinated pentachoron,
expanded pentachoron,
tetaco gyrobicupola,
vertex figure of cypit
 
 ©
Cross sections
 ©
Circumradius 1
Vertex figure
 ©
Vertex layers
LayerSymmetrySubsymmetries
 o3o3o3o o3o3o . o3o . o o . o3o . o3o3o
1x3o3o3x 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 50510
duhd 05100
spid 001020
& others)
Dihedral angles
  • at {4} between trip and trip:   arccos(-2/3) = 131.810315°
  • at {3} between tet and trip:   arccos(-sqrt(3/8)) = 127.761244°
Dual m3o3o3m
Confer
compounds:
dopix  
related segmentochora:
tet || co   tet || tricu   {6} || trip  
related CRFs:
gyspid  
decompositions:
spidpy  
general polytopal classes:
bistratic lace towers  
External
links
hedrondude   wikipedia   WikiChoron   quickfur

Note that spid can be thought of as the external blend of 10 pens + 20 trippies. This decomposition is described as the degenerate segmentoteron ox3oo3oo3ox&#x.


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

snubbed forms: β3o3o3x, β3o3o3β

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

x(ou)x x(xo)o3o(xo)x&#xt   → both heights = sqrt(5/12) = 0.645497
(trip || compound of pseudo {6} with perp pseudo u-line || gyro trip)

o(..). o(..).3o(..).     | 6 * * * | 1 2  2 1 0 0  0 0 0 0 | 2 1 2 2 1 2  2 0 0 0 0 0 0 | 1 2 1 1 2 1 0 0 0 0
.(o.). .(o.).3.(o.).     | * 6 * * | 0 0  2 0 1 1  2 0 0 0 | 0 0 1 2 2 0  2 1 2 2 0 0 0 | 0 1 1 0 2 2 1 1 0 0
.(.o). .(.o).3.(.o).     | * * 2 * | 0 0  0 3 0 0  0 3 0 0 | 0 0 0 0 0 3  6 0 0 0 3 0 0 | 0 0 0 1 3 3 0 0 1 0
.(..)o .(..)o3.(..)o     | * * * 6 | 0 0  0 0 0 0  2 1 1 2 | 0 0 0 0 0 0  2 2 1 2 2 2 1 | 0 0 0 0 1 2 1 2 1 1
-------------------------+---------+-----------------------+----------------------------+--------------------
x(..). .(..). .(..).     | 2 0 0 0 | 3 *  * * * *  * * * * | 2 0 2 0 0 0  0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 0
.(..). x(..). .(..).     | 2 0 0 0 | * 6  * * * *  * * * * | 1 1 0 1 0 1  0 0 0 0 0 0 0 | 1 1 0 1 1 0 0 0 0 0
o(o.). o(o.).3o(o.).&#x  | 1 1 0 0 | * * 12 * * *  * * * * | 0 0 1 1 1 0  1 0 0 0 0 0 0 | 0 1 1 0 1 1 0 0 0 0
o(.o). o(.o).3o(.o).&#x  | 1 0 1 0 | * *  * 6 * *  * * * * | 0 0 0 0 0 2  2 0 0 0 0 0 0 | 0 0 0 1 2 1 0 0 0 0
.(..). .(x.). .(..).     | 0 2 0 0 | * *  * * 3 *  * * * * | 0 0 0 2 0 0  0 0 2 0 0 0 0 | 0 1 0 0 2 0 1 0 0 0
.(..). .(..). .(x.).     | 0 2 0 0 | * *  * * * 3  * * * * | 0 0 0 0 2 0  0 0 0 2 0 0 0 | 0 0 1 0 0 2 0 1 0 0
.(o.)o .(o.)o3.(o.)o&#x  | 0 1 0 1 | * *  * * * * 12 * * * | 0 0 0 0 0 0  1 1 1 1 0 0 0 | 0 0 0 0 1 1 1 1 0 0
.(.o)o .(.o)o3.(.o)o&#x  | 0 0 1 1 | * *  * * * *  * 6 * * | 0 0 0 0 0 0  2 0 0 0 2 0 0 | 0 0 0 0 1 2 0 0 1 0
.(..)x .(..). .(..).     | 0 0 0 2 | * *  * * * *  * * 3 * | 0 0 0 0 0 0  0 2 0 0 0 2 0 | 0 0 0 0 0 0 1 2 0 1
.(..). .(..). .(..)x     | 0 0 0 2 | * *  * * * *  * * * 6 | 0 0 0 0 0 0  0 0 0 1 1 1 1 | 0 0 0 0 0 1 0 1 1 1
-------------------------+---------+-----------------------+----------------------------+--------------------
x(..). x(..). .(..).     | 4 0 0 0 | 2 2  0 0 0 0  0 0 0 0 | 3 * * * * *  * * * * * * * | 1 1 0 0 0 0 0 0 0 0
.(..). x(..).3o(..).     | 3 0 0 0 | 0 3  0 0 0 0  0 0 0 0 | * 2 * * * *  * * * * * * * | 1 0 0 1 0 0 0 0 0 0
x(o.). .(..). .(..).&#x  | 2 1 0 0 | 1 0  2 0 0 0  0 0 0 0 | * * 6 * * *  * * * * * * * | 0 1 1 0 0 0 0 0 0 0
.(..). x(x.). .(..).&#x  | 2 2 0 0 | 0 1  2 0 1 0  0 0 0 0 | * * * 6 * *  * * * * * * * | 0 1 0 0 1 0 0 0 0 0
.(..). .(..). o(x.).&#x  | 1 2 0 0 | 0 0  2 0 0 1  0 0 0 0 | * * * * 6 *  * * * * * * * | 0 0 1 0 0 1 0 0 0 0
.(..). x(.o). .(..).&#x  | 2 0 1 0 | 0 1  0 2 0 0  0 0 0 0 | * * * * * 6  * * * * * * * | 0 0 0 1 1 0 0 0 0 0
o(oo)o o(oo)o3o(oo)o&#xr | 1 1 1 1 | 0 0  1 1 0 0  1 1 0 0 | * * * * * * 12 * * * * * * | 0 0 0 0 1 1 0 0 0 0
.(o.)x .(..). .(..).&#x  | 0 1 0 2 | 0 0  0 0 0 0  2 0 1 0 | * * * * * *  * 6 * * * * * | 0 0 0 0 0 0 1 1 0 0
.(..). .(x.)o .(..).&#x  | 0 2 0 1 | 0 0  0 0 1 0  2 0 0 0 | * * * * * *  * * 6 * * * * | 0 0 0 0 1 0 1 0 0 0
.(..). .(..). .(x.)x&#x  | 0 2 0 2 | 0 0  0 0 0 1  2 0 0 1 | * * * * * *  * * * 6 * * * | 0 0 0 0 0 1 0 1 0 0
.(..). .(..). .(.o)x&#x  | 0 0 1 2 | 0 0  0 0 0 0  0 2 0 1 | * * * * * *  * * * * 6 * * | 0 0 0 0 0 1 0 0 1 0
.(..)x .(..). .(..)x     | 0 0 0 4 | 0 0  0 0 0 0  0 0 2 2 | * * * * * *  * * * * * 3 * | 0 0 0 0 0 0 0 1 0 1
.(..). .(..)o3.(..)x     | 0 0 0 3 | 0 0  0 0 0 0  0 0 0 3 | * * * * * *  * * * * * * 2 | 0 0 0 0 0 0 0 0 1 1
-------------------------+---------+-----------------------+----------------------------+--------------------
x(..). x(..).3o(..).      6 0 0 0 | 3 6  0 0 0 0  0 0 0 0 | 3 2 0 0 0 0  0 0 0 0 0 0 0 | 1 * * * * * * * * *
x(o.). x(x.). .(..).&#x   4 2 0 0 | 2 2  4 0 1 0  0 0 0 0 | 1 0 2 2 0 0  0 0 0 0 0 0 0 | * 3 * * * * * * * *
x(o.). .(..). o(x.).&#x   2 2 0 0 | 1 0  4 0 0 1  0 0 0 0 | 0 0 2 0 2 0  0 0 0 0 0 0 0 | * * 3 * * * * * * *
.(..). x(.o).3o(.o).&#x   3 0 1 0 | 0 3  0 3 0 0  0 0 0 0 | 0 1 0 0 0 3  0 0 0 0 0 0 0 | * * * 2 * * * * * *
.(..). x(xo)o .(..).&#xr  2 2 1 1 | 0 1  2 2 1 0  2 1 0 0 | 0 0 0 1 0 1  2 0 1 0 0 0 0 | * * * * 6 * * * * *
.(..). .(..). o(xo)x&#xr  1 2 1 2 | 0 0  2 1 0 1  2 2 0 1 | 0 0 0 0 1 0  2 0 0 1 1 0 0 | * * * * * 6 * * * *
.(o.)x .(x.)o .(..).&#x   0 2 0 2 | 0 0  0 0 1 0  4 0 1 0 | 0 0 0 0 0 0  0 2 2 0 0 0 0 | * * * * * * 3 * * *
.(o.)x .(..). .(x.)x&#x   0 2 0 4 | 0 0  0 0 0 1  4 0 2 2 | 0 0 0 0 0 0  0 2 0 2 0 1 0 | * * * * * * * 3 * *
.(..). .(.o)o3.(.o)x&#x   0 0 1 3 | 0 0  0 0 0 0  0 3 0 3 | 0 0 0 0 0 0  0 0 0 0 3 0 1 | * * * * * * * * 2 *
.(..)x .(..)o3.(..)x      0 0 0 6 | 0 0  0 0 0 0  0 0 3 6 | 0 0 0 0 0 0  0 0 0 0 0 3 2 | * * * * * * * * * 1

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