Acronym octatoe, oct || toe
Name (degenerate) octahedron atop truncated octahedron
 
tO  truncated octahedron ©
Segmentochoron display
Circumradius ∞   i.e. flat in euclidean space
Dihedral angles
Confer
general polytopal classes:
segmentochora   lace simplices   decomposition  

It either can be thought of as a degenerate 4D segmentotope with zero height, or as a 3D euclidean decomposition of the larger base into smaller bits.


Incidence matrix according to Dynkin symbol

xx3ox4oo&#x   → height = 0
(oct || toe)

o.3o.4o.    | 6  *   4  4  0  0 | 4  4  4 0 0 | 1 4 1 0
.o3.o4.o    | * 24 |  0  1  1  2 | 0  1  2 2 1 | 0 2 1 1
------------+------+-------------+-------------+--------
x. .. ..    | 2  0 | 12  *  *  * | 2  1  0 0 0 | 1 2 0 0
oo3oo4oo&#x | 1  1 |  * 24  *  * | 0  1  2 0 0 | 0 2 1 0
.x .. ..    | 0  2 |  *  * 12  * | 0  1  0 2 0 | 0 2 0 1
.. .x ..    | 0  2 |  *  *  * 24 | 0  0  1 1 1 | 0 1 1 1
------------+------+-------------+-------------+--------
x.3o. ..    | 3  0 |  3  0  0  0 | 8  *  * * * | 1 1 0 0
xx .. ..&#x | 2  2 |  1  2  1  0 | * 12  * * * | 0 2 0 0
.. ox ..&#x | 1  2 |  0  2  0  1 | *  * 24 * * | 0 1 1 0
.x3.x ..    | 0  6 |  0  0  3  3 | *  *  * 8 * | 0 1 0 1
.. .x4.o    | 0  4 |  0  0  0  4 | *  *  * * 6 | 0 0 1 1
------------+------+-------------+-------------+--------
x.3o.4o.     6  0 | 12  0  0  0 | 8  0  0 0 0 | 1 * * *
xx3ox ..&#x  3  6 |  3  6  3  3 | 1  3  3 1 0 | * 8 * *
.. ox4oo&#x  1  4 |  0  4  0  4 | 0  0  4 0 1 | * * 6 *
.x3.x4.o     0 24 |  0  0 12 24 | 0  0  0 8 6 | * * * 1

ox3xx3ox&#x   → height = 0
(oct || toe)

o.3o.3o.    | 6  *   4  4  0  0  0 | 2 2  2  4  2 0 0 0 | 1 2 1 2 0
.o3.o3.o    | * 24 |  0  1  1  1  1 | 0 0  1  1  1 1 1 1 | 0 1 1 1 1
------------+------+----------------+--------------------+----------
.. x. ..    | 2  0 | 12  *  *  *  * | 1 1  0  1  0 0 0 0 | 1 1 0 1 0
oo3oo3oo&#x | 1  1 |  * 24  *  *  * | 0 0  1  1  1 0 0 0 | 0 1 1 1 0
.x .. ..    | 0  2 |  *  * 12  *  * | 0 0  1  0  0 1 1 0 | 0 1 1 0 1
.. .x ..    | 0  2 |  *  *  * 12  * | 0 0  0  1  0 1 0 1 | 0 1 0 1 1
.. .. .x    | 0  2 |  *  *  *  * 12 | 0 0  0  0  1 0 1 1 | 0 0 1 1 1
------------+------+----------------+--------------------+----------
o.3x. ..    | 3  0 |  3  0  0  0  0 | 4 *  *  *  * * * * | 1 1 0 0 0
.. x.3o.    | 3  0 |  3  0  0  0  0 | * 4  *  *  * * * * | 1 0 0 1 0
ox .. ..&#x | 1  2 |  0  2  1  0  0 | * * 12  *  * * * * | 0 1 1 0 0
.. xx ..&#x | 2  2 |  1  2  0  1  0 | * *  * 12  * * * * | 0 1 0 1 0
.. .. ox&#x | 1  2 |  0  2  0  0  1 | * *  *  * 12 * * * | 0 0 1 1 0
.x3.x ..    | 0  6 |  0  0  3  3  0 | * *  *  *  * 4 * * | 0 1 0 0 1
.x .. .x    | 0  4 |  0  0  2  0  2 | * *  *  *  * * 6 * | 0 0 1 0 1
.. .x3.x    | 0  6 |  0  0  0  3  3 | * *  *  *  * * * 4 | 0 0 0 1 1
------------+------+----------------+--------------------+----------
o.3x.3o.     6  0 | 12  0  0  0  0 | 4 4  0  0  0 0 0 0 | 1 * * * *
ox3xx ..&#x  3  6 |  3  6  3  3  0 | 1 0  3  3  0 1 0 0 | * 4 * * *
ox .. ox&#x  1  4 |  0  4  2  0  2 | 0 0  2  0  2 0 1 0 | * * 6 * *
.. xx3ox&#x  3  6 |  3  6  0  3  3 | 0 1  0  3  3 0 0 1 | * * * 4 *
.x3.x3.x     0 24 |  0  0 12 12 12 | 0 0  0  0  0 4 6 4 | * * * * 1

© 2004-2019
top of page