Acronym cope, K-4.43
Name cuboctahedron prism
Segmentochoron display
Cross sections
 ©
Circumradius sqrt(5)/2 = 1.118034
Coordinates (1/sqrt(2), 1/sqrt(2), 0, 1/2)   & all permutations in all but last coord., all changes of sign
General of army (is itself convex)
Colonel of regiment (is itself locally convex – uniform polychoral members:
by cells: cho co cube hip oho trip
chope 206400
cope 026008
ohope 000428
)
Dihedral angles
  • at {4} between cube and trip:   arccos(-1/sqrt(3)) = 125.264390°
  • at {4} between co and cube:   90°
  • at {3} between co and trip:   90°
Confer
related CRFs:
oct || co || co || oct  
related segmentochora:
tricupe  
general polytopal classes:
segmentochora   bistratic lace towers  
External
links
hedrondude   wikipedia

Incidence matrix according to Dynkin symbol

x o3x4o

. . . . | 24   1  4 |  4  2  2 | 2 2 1
--------+----+-------+----------+------
x . . . |  2 | 12  * |  4  0  0 | 2 2 0
. . x . |  2 |  * 48 |  1  1  1 | 1 1 1
--------+----+-------+----------+------
x . x . |  4 |  2  2 | 24  *  * | 1 1 0
. o3x . |  3 |  0  3 |  * 16  * | 1 0 1
. . x4o |  4 |  0  4 |  *  * 12 | 0 1 1
--------+----+-------+----------+------
x o3x .   6 |  3  6 |  3  2  0 | 8 * *
x . x4o   8 |  4  8 |  4  0  2 | * 6 *
. o3x4o  12 |  0 24 |  0  8  6 | * * 2

x o3x4/3o

. . .   . | 24   1  4 |  4  2  2 | 2 2 1
----------+----+-------+----------+------
x . .   . |  2 | 12  * |  4  0  0 | 2 2 0
. . x   . |  2 |  * 48 |  1  1  1 | 1 1 1
----------+----+-------+----------+------
x . x   . |  4 |  2  2 | 24  *  * | 1 1 0
. o3x   . |  3 |  0  3 |  * 16  * | 1 0 1
. . x4/3o |  4 |  0  4 |  *  * 12 | 0 1 1
----------+----+-------+----------+------
x o3x   .   6 |  3  6 |  3  2  0 | 8 * *
x . x4/3o   8 |  4  8 |  4  0  2 | * 6 *
. o3x4/3o  12 |  0 24 |  0  8  6 | * * 2

x o3/2x4o

. .   . . | 24   1  4 |  4  2  2 | 2 2 1
----------+----+-------+----------+------
x .   . . |  2 | 12  * |  4  0  0 | 2 2 0
. .   x . |  2 |  * 48 |  1  1  1 | 1 1 1
----------+----+-------+----------+------
x .   x . |  4 |  2  2 | 24  *  * | 1 1 0
. o3/2x . |  3 |  0  3 |  * 16  * | 1 0 1
. .   x4o |  4 |  0  4 |  *  * 12 | 0 1 1
----------+----+-------+----------+------
x o3/2x .   6 |  3  6 |  3  2  0 | 8 * *
x .   x4o   8 |  4  8 |  4  0  2 | * 6 *
. o3/2x4o  12 |  0 24 |  0  8  6 | * * 2

x o3/2x4/3o

. .   .   . | 24   1  4 |  4  2  2 | 2 2 1
------------+----+-------+----------+------
x .   .   . |  2 | 12  * |  4  0  0 | 2 2 0
. .   x   . |  2 |  * 48 |  1  1  1 | 1 1 1
------------+----+-------+----------+------
x .   x   . |  4 |  2  2 | 24  *  * | 1 1 0
. o3/2x   . |  3 |  0  3 |  * 16  * | 1 0 1
. .   x4/3o |  4 |  0  4 |  *  * 12 | 0 1 1
------------+----+-------+----------+------
x o3/2x   .   6 |  3  6 |  3  2  0 | 8 * *
x .   x4/3o   8 |  4  8 |  4  0  2 | * 6 *
. o3/2x4/3o  12 |  0 24 |  0  8  6 | * * 2

x x3o3x

. . . . | 24   1  2  2 |  2  2 1  2 1 | 1 2 1 1
--------+----+----------+--------------+--------
x . . . |  2 | 12  *  * |  2  2 0  0 0 | 1 2 1 0
. x . . |  2 |  * 24  * |  1  0 1  1 0 | 1 1 0 1
. . . x |  2 |  *  * 24 |  0  1 0  1 1 | 0 1 1 1
--------+----+----------+--------------+--------
x x . . |  4 |  2  2  0 | 12  * *  * * | 1 1 0 0
x . . x |  4 |  2  0  2 |  * 12 *  * * | 0 1 1 0
. x3o . |  3 |  0  3  0 |  *  * 8  * * | 1 0 0 1
. x . x |  4 |  0  2  2 |  *  * * 12 * | 0 1 0 1
. . o3x |  3 |  0  0  3 |  *  * *  * 8 | 0 0 1 1
--------+----+----------+--------------+--------
x x3o .   6 |  3  6  0 |  3  0 2  0 0 | 4 * * *
x x . x   8 |  4  4  4 |  2  2 0  2 0 | * 6 * *
x . o3x   6 |  3  0  6 |  0  3 0  0 2 | * * 4 *
. x3o3x  12 |  0 12 12 |  0  0 4  6 4 | * * * 2

x x3/2o3/2x

. .   .   . | 24   1  2  2 |  2  2 1  2 1 | 1 2 1 1
------------+----+----------+--------------+--------
x .   .   . |  2 | 12  *  * |  2  2 0  0 0 | 1 2 1 0
. x   .   . |  2 |  * 24  * |  1  0 1  1 0 | 1 1 0 1
. .   .   x |  2 |  *  * 24 |  0  1 0  1 1 | 0 1 1 1
------------+----+----------+--------------+--------
x x   .   . |  4 |  2  2  0 | 12  * *  * * | 1 1 0 0
x .   .   x |  4 |  2  0  2 |  * 12 *  * * | 0 1 1 0
. x3/2o   . |  3 |  0  3  0 |  *  * 8  * * | 1 0 0 1
. x   .   x |  4 |  0  2  2 |  *  * * 12 * | 0 1 0 1
. .   o3/2x |  3 |  0  0  3 |  *  * *  * 8 | 0 0 1 1
------------+----+----------+--------------+--------
x x3/2o   .   6 |  3  6  0 |  3  0 2  0 0 | 4 * * *
x x   .   x   8 |  4  4  4 |  2  2 0  2 0 | * 6 * *
x .   o3/2x   6 |  3  0  6 |  0  3 0  0 2 | * * 4 *
. x3/2o3/2x  12 |  0 12 12 |  0  0 4  6 4 | * * * 2

oo3xx4oo&#x   → height = 1
(co || co)

o.3o.4o.    | 12  *   4  1  0 | 2 2  4 0 0 | 1 2 2 0
.o3.o4.o    |  * 12   0  1  4 | 0 0  4 2 2 | 0 2 2 1
------------+-------+----------+------------+--------
.. x. ..    |  2  0 | 24  *  * | 1 1  1 0 0 | 1 1 1 0
oo3oo4oo&#x |  1  1 |  * 12  * | 0 0  4 0 0 | 0 2 2 0
.. .x ..    |  0  2 |  *  * 24 | 0 0  1 1 1 | 0 1 1 1
------------+-------+----------+------------+--------
o.3x. ..    |  3  0 |  3  0  0 | 8 *  * * * | 1 1 0 0
.. x.4o.    |  4  0 |  4  0  0 | * 6  * * * | 1 0 1 0
.. xx ..&#x |  2  2 |  1  2  1 | * * 24 * * | 0 1 1 0
.o3.x ..    |  0  3 |  0  0  3 | * *  * 8 * | 0 1 0 1
.. .x4.o    |  0  4 |  0  0  4 | * *  * * 6 | 0 0 1 1
------------+-------+----------+------------+--------
o.3x.4o.     12  0 | 24  0  0 | 8 6  0 0 0 | 1 * * *
oo3xx ..&#x   3  3 |  3  3  3 | 1 0  3 1 0 | * 8 * *
.. xx4oo&#x   4  4 |  4  4  4 | 0 1  4 0 1 | * * 6 *
.o3.x4.o      0 12 |  0  0 24 | 0 0  0 8 6 | * * * 1

xx3oo3xx&#x   → height = 1
(co || co)

o.3o.3o.    | 12  *   2  2  1  0  0 | 1 2 1  2  2 0 0 0 | 1 1 2 1 0
.o3.o3.o    |  * 12   0  0  1  2  2 | 0 0 0  2  2 1 2 1 | 0 1 2 1 1
------------+-------+----------------+-------------------+----------
x. .. ..    |  2  0 | 12  *  *  *  * | 1 1 0  1  0 0 0 0 | 1 1 1 0 0
.. .. x.    |  2  0 |  * 12  *  *  * | 0 1 1  0  1 0 0 0 | 1 0 1 1 0
oo3oo3oo&#x |  1  1 |  *  * 12  *  * | 0 0 0  2  2 0 0 0 | 0 1 2 1 0
.x .. ..    |  0  2 |  *  *  * 12  * | 0 0 0  1  0 1 1 0 | 0 1 1 0 1
.. .. .x    |  0  2 |  *  *  *  * 12 | 0 0 0  0  1 0 1 1 | 0 0 1 1 1
------------+-------+----------------+-------------------+----------
x.3o. ..    |  3  0 |  3  0  0  0  0 | 4 * *  *  * * * * | 1 1 0 0 0
x. .. x.    |  4  0 |  2  2  0  0  0 | * 6 *  *  * * * * | 1 0 1 0 0
.. o.3x.    |  3  0 |  0  3  0  0  0 | * * 4  *  * * * * | 1 0 0 1 0
xx .. ..&#x |  2  2 |  1  0  2  1  0 | * * * 12  * * * * | 0 1 1 0 0
.. .. xx&#x |  2  2 |  0  1  2  0  1 | * * *  * 12 * * * | 0 0 1 1 0
.x3.o ..    |  0  3 |  0  0  0  3  0 | * * *  *  * 4 * * | 0 1 0 0 1
.x .. .x    |  0  4 |  0  0  0  2  2 | * * *  *  * * 6 * | 0 0 1 0 1
.. .o3.x    |  0  3 |  0  0  0  0  3 | * * *  *  * * * 4 | 0 0 0 1 1
------------+-------+----------------+-------------------+----------
x.3o.3x.     12  0 | 12 12  0  0  0 | 4 6 4  0  0 0 0 0 | 1 * * * *
xx3oo ..&#x   3  3 |  3  0  3  3  0 | 1 0 0  3  0 1 0 0 | * 4 * * *
xx .. xx&#x   4  4 |  2  2  4  2  2 | 0 1 0  2  2 0 1 0 | * * 6 * *
.. oo3xx&#x   3  3 |  0  3  3  0  3 | 0 0 1  0  3 0 0 1 | * * * 4 *
.x3.o3.x      0 12 |  0  0  0 12 12 | 0 0 0  0  0 4 6 4 | * * * * 1

xxx xox4oqo&#xt   → both heights = 1/sqrt(2) = 0.707107
(cube || pseudo gyro (x,q)-cube || cube)

o.. o..4o..     | 8 * *  1 2  2 0  0 0 0 | 2 1 2 2 1 0 0 0 0 | 1 2 1 1 0 0
.o. .o.4.o.     | * 8 *  0 0  2 1  2 0 0 | 0 0 2 1 2 2 1 0 0 | 0 1 2 1 1 0
..o ..o4..o     | * * 8  0 0  0 0  2 1 2 | 0 0 0 0 1 2 2 2 1 | 0 0 1 1 2 1
----------------+-------+-----------------+-------------------+------------
x.. ... ...     | 2 0 0 | 4 *  * *  * * * | 2 0 2 0 0 0 0 0 0 | 1 2 1 0 0 0
... x.. ...     | 2 0 0 | * 8  * *  * * * | 1 1 0 1 0 0 0 0 0 | 1 1 0 1 0 0
oo. oo.4oo.&#x  | 1 1 0 | * * 16 *  * * * | 0 0 1 1 1 0 0 0 0 | 0 1 1 1 0 0
.x. ... ...     | 0 2 0 | * *  * 4  * * * | 0 0 2 0 0 2 0 0 0 | 0 1 2 0 1 0
.oo .oo4.oo&#x  | 0 1 1 | * *  * * 16 * * | 0 0 0 0 1 1 1 0 0 | 0 0 1 1 1 0
..x ... ...     | 0 0 2 | * *  * *  * 4 * | 0 0 0 0 0 2 0 2 0 | 0 0 1 0 2 1
... ..x ...     | 0 0 2 | * *  * *  * * 8 | 0 0 0 0 0 0 1 1 1 | 0 0 0 1 1 1
----------------+-------+-----------------+-------------------+------------
x.. x.. ...     | 4 0 0 | 2 2  0 0  0 0 0 | 4 * * * * * * * * | 1 1 0 0 0 0
... x..4o..     | 4 0 0 | 0 4  0 0  0 0 0 | * 2 * * * * * * * | 1 0 0 1 0 0
xx. ... ...&#x  | 2 2 0 | 1 0  2 1  0 0 0 | * * 8 * * * * * * | 0 1 1 0 0 0
... xo. ...&#x  | 2 1 0 | 0 1  2 0  0 0 0 | * * * 8 * * * * * | 0 1 0 1 0 0
... ... oqo&#xt | 1 2 1 | 0 0  2 0  2 0 0 | * * * * 8 * * * * | 0 0 1 1 0 0
.xx ... ...&#x  | 0 2 2 | 0 0  0 1  2 1 0 | * * * * * 8 * * * | 0 0 1 0 1 0
... .ox ...&#x  | 0 1 2 | 0 0  0 0  2 0 1 | * * * * * * 8 * * | 0 0 0 1 1 0
..x ..x ...     | 0 0 4 | 0 0  0 0  0 2 2 | * * * * * * * 4 * | 0 0 0 0 1 1
... ..x4..o     | 0 0 4 | 0 0  0 0  0 0 4 | * * * * * * * * 2 | 0 0 0 1 0 1
----------------+-------+-----------------+-------------------+------------
x.. x..4o..      8 0 0 | 4 8  0 0  0 0 0 | 4 2 0 0 0 0 0 0 0 | 1 * * * * *
xx. xo. ...&#x   4 2 0 | 2 2  4 1  0 0 0 | 1 0 2 2 0 0 0 0 0 | * 4 * * * *
xxx ... oqo&#xt  2 4 2 | 1 0  4 2  4 1 0 | 0 0 2 0 2 2 0 0 0 | * * 4 * * *
... xox4oqo&#xt  4 4 4 | 0 4  8 0  8 0 4 | 0 1 0 4 4 0 4 0 1 | * * * 2 * *
.xx .ox ...&#x   0 2 4 | 0 0  0 1  4 2 2 | 0 0 0 0 0 2 2 1 0 | * * * * 4 *
..x ..x4..o      0 0 8 | 0 0  0 0  0 4 8 | 0 0 0 0 0 0 0 4 2 | * * * * * 1
or
o.. o..4o..     & | 16 *  1  2  2 0 | 2 1  2  2 1 | 1 2 1 1
.o. .o.4.o.       |  * 8  0  0  4 1 | 0 0  4  2 2 | 0 2 2 1
------------------+------+-----------+-------------+--------
x.. ... ...     & |  2 0 | 8  *  * * | 2 0  2  0 0 | 1 2 1 0
... x.. ...     & |  2 0 | * 16  * * | 1 1  0  1 0 | 1 1 0 1
oo. oo.4oo.&#x  & |  1 1 | *  * 32 * | 0 0  1  1 1 | 0 1 1 1
.x. ... ...       |  0 2 | *  *  * 4 | 0 0  4  0 0 | 0 2 2 0
------------------+------+-----------+-------------+--------
x.. x.. ...     & |  4 0 | 2  2  0 0 | 8 *  *  * * | 1 1 0 0
... x..4o..     & |  4 0 | 0  4  0 0 | * 4  *  * * | 1 0 0 1
xx. ... ...&#x  & |  2 2 | 1  0  2 1 | * * 16  * * | 0 1 1 0
... xo. ...&#x  & |  2 1 | 0  1  2 0 | * *  * 16 * | 0 1 0 1
... ... oqo&#xt   |  2 2 | 0  0  4 0 | * *  *  * 8 | 0 0 1 1
------------------+------+-----------+-------------+--------
x.. x..4o..     &   8 0 | 4  8  0 0 | 4 2  0  0 0 | 2 * * *
xx. xo. ...&#x  &   4 2 | 2  2  4 1 | 1 0  2  2 0 | * 8 * *
xxx ... oqo&#xt     4 4 | 2  0  8 2 | 0 0  4  0 2 | * * 4 *
... xox4oqo&#xt     8 4 | 0  8 16 0 | 0 2  0  8 4 | * * * 2

xxx xxo3oxx&#xt   → both heights = sqrt(2/3) = 0.816497
(trip || pseudo hip || inv trip)

o.. o..3o..     | 6  * *  1 2  2 0 0 0  0 0 0 | 2 1 2 2 1 0 0 0 0 0 0 0 | 1 2 1 1 0 0 0
.o. .o.3.o.     | * 12 *  0 0  1 1 1 1  1 0 0 | 0 0 1 1 1 1 1 1 1 1 0 0 | 0 1 1 1 1 1 0
..o ..o3..o     | *  * 6  0 0  0 0 0 0  2 1 2 | 0 0 0 0 0 0 0 1 2 2 2 1 | 0 0 0 1 1 2 1
----------------+--------+---------------------+-------------------------+--------------
x.. ... ...     | 2  0 0 | 3 *  * * * *  * * * | 2 0 2 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0
... x.. ...     | 2  0 0 | * 6  * * * *  * * * | 1 1 0 1 0 0 0 0 0 0 0 0 | 1 1 0 1 0 0 0
oo. oo.3oo.&#x  | 1  1 0 | * * 12 * * *  * * * | 0 0 1 1 1 0 0 0 0 0 0 0 | 0 1 1 1 0 0 0
.x. ... ...     | 0  2 0 | * *  * 6 * *  * * * | 0 0 1 0 0 1 1 1 0 0 0 0 | 0 1 1 0 1 1 0
... .x. ...     | 0  2 0 | * *  * * 6 *  * * * | 0 0 0 1 0 1 0 0 1 0 0 0 | 0 1 0 1 1 0 0
... ... .x.     | 0  2 0 | * *  * * * 6  * * * | 0 0 0 0 1 0 1 0 0 1 0 0 | 0 0 1 1 0 1 0
.oo .oo3.oo&#x  | 0  1 1 | * *  * * * * 12 * * | 0 0 0 0 0 0 0 1 1 1 0 0 | 0 0 0 1 1 1 0
..x ... ...     | 0  0 2 | * *  * * * *  * 3 * | 0 0 0 0 0 0 0 2 0 0 2 0 | 0 0 0 0 1 2 1
... ... ..x     | 0  0 2 | * *  * * * *  * * 6 | 0 0 0 0 0 0 0 0 0 1 1 1 | 0 0 0 1 0 1 1
----------------+--------+---------------------+-------------------------+--------------
x.. x.. ...     | 4  0 0 | 2 2  0 0 0 0  0 0 0 | 3 * * * * * * * * * * * | 1 1 0 0 0 0 0
... x..3o..     | 3  0 0 | 0 3  0 0 0 0  0 0 0 | * 2 * * * * * * * * * * | 1 0 0 1 0 0 0
xx. ... ...&#x  | 2  2 0 | 1 0  2 1 0 0  0 0 0 | * * 6 * * * * * * * * * | 0 1 1 0 0 0 0
... xx. ...&#x  | 2  2 0 | 0 1  2 0 1 0  0 0 0 | * * * 6 * * * * * * * * | 0 1 0 1 0 0 0
... ... ox.&#x  | 1  2 0 | 0 0  2 0 0 1  0 0 0 | * * * * 6 * * * * * * * | 0 0 1 1 0 0 0
.x. .x. ...     | 0  4 0 | 0 0  0 2 2 0  0 0 0 | * * * * * 3 * * * * * * | 0 1 0 0 1 0 0
.x. ... .x.     | 0  4 0 | 0 0  0 2 0 2  0 0 0 | * * * * * * 3 * * * * * | 0 0 1 0 0 1 0
.xx ... ...&#x  | 0  2 1 | 0 0  0 1 0 0  2 1 0 | * * * * * * * 6 * * * * | 0 0 0 0 1 1 0
... .xo ...&#x  | 0  2 2 | 0 0  0 0 1 0  2 0 0 | * * * * * * * * 6 * * * | 0 0 0 1 1 0 0
... ... .xx&#x  | 0  2 2 | 0 0  0 0 0 1  2 0 1 | * * * * * * * * * 6 * * | 0 0 0 1 0 1 0
..x ... ..x     | 0  0 4 | 0 0  0 0 0 0  0 2 2 | * * * * * * * * * * 3 * | 0 0 0 0 0 1 1
... ..o3..x     | 0  0 3 | 0 0  0 0 0 0  0 0 3 | * * * * * * * * * * * 2 | 0 0 0 1 0 0 1
----------------+--------+---------------------+-------------------------+--------------
x.. x..3o..      6  0 0 | 3 6  0 0 0 0  0 0 0 | 3 2 0 0 0 0 0 0 0 0 0 0 | 1 * * * * * *
xx. xx. ...&#x   4  4 0 | 2 2  4 2 2 0  0 0 0 | 1 0 2 2 0 1 0 0 0 0 0 0 | * 3 * * * * *
xx. ... ox.&#x   2  4 0 | 1 0  4 2 0 2  0 0 0 | 0 0 2 0 2 0 1 0 0 0 0 0 | * * 3 * * * *
... xxo3oxx&#xt  3  6 3 | 0 3  6 0 3 3  6 0 3 | 0 1 0 3 3 0 0 0 3 3 0 1 | * * * 2 * * *
.xx .xo ...&#x   0  4 2 | 0 0  0 2 2 0  4 1 0 | 0 0 0 0 0 1 0 2 2 0 0 0 | * * * * 3 * *
.xx ... .xx&#x   0  4 4 | 0 0  0 2 0 2  4 2 2 | 0 0 0 0 0 0 1 2 0 2 1 0 | * * * * * 3 *
..x ..o3..x      0  0 6 | 0 0  0 0 0 0  0 3 6 | 0 0 0 0 0 0 0 0 0 0 3 2 | * * * * * * 1
or
o.. o..3o..     & | 12  *  1  2  2 0  0 | 2 1  2  2  1 0 | 1 2 1 1
.o. .o.3.o.       |  * 12  0  0  2 1  2 | 0 0  2  2  2 2 | 0 2 2 1
------------------+-------+--------------+----------------+--------
x.. ... ...     & |  2  0 | 6  *  * *  * | 2 0  2  0  0 0 | 1 2 1 0
... x.. ...     & |  2  0 | * 12  * *  * | 1 1  0  1  0 0 | 1 1 0 1
oo. oo.3oo.&#x  & |  1  1 | *  * 24 *  * | 0 0  1  1  1 0 | 0 1 1 1
.x. ... ...       |  0  2 | *  *  * 6  * | 0 0  2  0  0 2 | 0 2 2 0
... .x. ...     & |  0  2 | *  *  * * 12 | 0 0  0  1  1 1 | 0 1 1 1
------------------+-------+--------------+----------------+--------
x.. x.. ...     & |  4  0 | 2  2  0 0  0 | 6 *  *  *  * * | 1 1 0 0
... x..3o..     & |  3  0 | 0  3  0 0  0 | * 4  *  *  * * | 1 0 0 1
xx. ... ...&#x  & |  2  2 | 1  0  2 1  0 | * * 12  *  * * | 0 1 1 0
... xx. ...&#x  & |  2  2 | 0  1  2 0  1 | * *  * 12  * * | 0 1 0 1
... ... ox.&#x  & |  1  2 | 0  0  2 0  1 | * *  *  * 12 * | 0 0 1 1
.x. .x. ...     & |  0  4 | 0  0  0 2  2 | * *  *  *  * 6 | 0 1 1 0
------------------+-------+--------------+----------------+--------
x.. x..3o..     &   6  0 | 3  6  0 0  0 | 3 2  0  0  0 0 | 2 * * *
xx. xx. ...&#x  &   4  4 | 2  2  4 2  2 | 1 0  2  2  0 1 | * 6 * *
xx. ... ox.&#x  &   2  4 | 1  0  4 2  2 | 0 0  2  0  2 1 | * * 6 *
... xxo3oxx&#xt     6  6 | 0  6 12 0  6 | 0 2  0  6  6 0 | * * * 2

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