Acronym octu
Name axially-octahedral ursachoron ofx3xoo4ooo&#xt,
oct-based ursulate,
vertex figure of s3s4o3o4o
 
 ©
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Circumradius sqrt[3+sqrt(5)]/2 = 1.144123
Coordinates
    • (1/sqrt(2), 0, 0; sqrt(f/2))                            & all permutations in first 3 coord.s & all changes of sign in first 3 coord.s
    (layer x3o4o in lace tower description)
    • (f/sqrt(2), 0, 0; 0)                                       & all permutations in first 3 coord.s & all changes of sign in first 3 coord.s
    (layer f3o4o in lace tower description)
    • (1/sqrt(2), 1/sqrt(2), 0; -1/sqrt(2f))             & all permutations in first 3 coord.s & all changes of sign in first 3 coord.s
    (layer o3x4o in lace tower description)
where f=(1+sqrt(5))/2   &   circumcenter is at origin
Confer
related CRFs:
tetu   iku   xoBo3ofox3xooo&#xt  
general polytopal classes:
ursatopes   bistratic lace towers  
External
links
quickfur

Incidence matrix according to Dynkin symbol

ofx3xoo4ooo&#xt   → height(1,2) = sqrt[sqrt(5)-1]/2 = 0.555893
                    height(2,3) = sqrt[1+sqrt(5)]/2 = 0.899454
(co || pseudo f-oct || oct)

o..3o..4o..     | 12 * * |  4  2 0  0 | 2 2  1  4 0 | 1 2 2 0
.o.3.o.4.o.     |  * 6 * |  0  4 1  0 | 0 0  4  4 0 | 0 4 1 0
..o3..o4..o     |  * * 6 |  0  0 1  4 | 0 0  4  0 4 | 0 4 0 1
----------------+--------+------------+-------------+--------
... x.. ...     |  2 0 0 | 24  * *  * | 1 1  0  1 0 | 1 1 1 0
oo.3oo.4oo.&#x  |  1 1 0 |  * 24 *  * | 0 0  1  2 0 | 0 2 1 0
.oo3.oo4.oo&#x  |  0 1 1 |  *  * 6  * | 0 0  4  0 0 | 0 4 0 0
..x ... ...     |  0 0 2 |  *  * * 12 | 0 0  1  0 2 | 0 2 0 1
----------------+--------+------------+-------------+--------
o..3x.. ...     |  3 0 0 |  3  0 0  0 | 8 *  *  * * | 1 1 0 0
... x..4o..     |  4 0 0 |  4  0 0  0 | * 6  *  * * | 1 0 1 0
ofx ... ...&#xt |  1 2 2 |  0  2 2  1 | * * 12  * * | 0 2 0 0
... xo. ...&#x  |  2 1 0 |  1  2 0  0 | * *  * 24 * | 0 1 1 0
..x3..o ...     |  0 0 3 |  0  0 0  3 | * *  *  * 8 | 0 1 0 1
----------------+--------+------------+-------------+--------
o..3x..4o..      12 0 0 | 24  0 0  0 | 8 6  0  0 0 | 1 * * *
ofx3xoo ...&#xt   3 3 3 |  3  6 3  3 | 1 0  3  3 1 | * 8 * *
... xo.4oo.&#x    4 1 0 |  4  4 0  0 | 0 1  0  4 0 | * * 6 *
..x3..o4..o       0 0 6 |  0  0 0 12 | 0 0  0  0 8 | * * * 1

xoo3ofx3xoo&#xt   → height(1,2) = sqrt[sqrt(5)-1]/2 = 0.555893
                    height(2,3) = sqrt[1+sqrt(5)]/2 = 0.899454
(co || pseudo f-oct || oct)

o..3o..3o..     | 12 * * |  2  2  2 0  0 | 1 2 1  2  1  2 0 0 | 1 1 2 1 0
.o.3.o.3.o.     |  * 6 * |  0  0  4 1  0 | 0 0 0  2  4  2 0 0 | 0 2 1 2 0
..o3..o3..o     |  * * 6 |  0  0  0 1  4 | 0 0 0  0  4  0 2 2 | 0 2 0 2 1
----------------+--------+---------------+--------------------+----------
x.. ... ...     |  2 0 0 | 12  *  * *  * | 1 1 0  1  0  0 0 0 | 1 1 1 0 0
... ... x..     |  2 0 0 |  * 12  * *  * | 0 1 1  0  0  1 0 0 | 1 0 1 1 0
oo.3oo.3oo.&#x  |  1 1 0 |  *  * 24 *  * | 0 0 0  1  1  1 0 0 | 0 1 1 1 0
.oo3.oo3.oo&#x  |  0 1 1 |  *  *  * 6  * | 0 0 0  0  4  0 0 0 | 0 2 0 2 0
... ..x ...     |  0 0 2 |  *  *  * * 12 | 0 0 0  0  1  0 1 1 | 0 1 0 1 1
----------------+--------+---------------+--------------------+----------
x..3o.. ...     |  3 0 0 |  3  0  0 0  0 | 4 * *  *  *  * * * | 1 1 0 0 0
x.. ... x..     |  4 0 0 |  2  2  0 0  0 | * 6 *  *  *  * * * | 1 0 1 0 0
... o..3x..     |  3 0 0 |  0  3  0 0  0 | * * 4  *  *  * * * | 1 0 0 1 0
xo. ... ...&#x  |  2 1 0 |  1  0  2 0  0 | * * * 12  *  * * * | 0 1 1 0 0
... ofx ...&#xt |  1 2 2 |  0  0  2 2  1 | * * *  * 12  * * * | 0 1 0 1 0
... ... xo.&#x  |  2 1 0 |  0  1  2 0  0 | * * *  *  * 12 * * | 0 0 1 1 0
..o3..x ...     |  0 0 3 |  0  0  0 0  3 | * * *  *  *  * 4 * | 0 1 0 0 1
... ..x3..o     |  0 0 3 |  0  0  0 0  3 | * * *  *  *  * * 4 | 0 0 0 1 1
----------------+--------+---------------+--------------------+----------
x..3o..3x..      12 0 0 | 12 12  0 0  0 | 4 6 4  0  0  0 0 0 | 1 * * * *
xoo3ofx ...&#xt   3 3 3 |  3  0  6 3  3 | 1 0 0  3  3  0 1 0 | * 4 * * *
xo. ... xo.&#x    4 1 0 |  2  2  4 0  0 | 0 1 0  2  0  2 0 0 | * * 6 * *
... ofx3xoo&#xt   3 3 3 |  0  3  6 3  3 | 0 0 1  0  3  3 0 1 | * * * 4 *
..o3..x3..o       0 0 6 |  0  0  0 0 12 | 0 0 0  0  0  0 4 4 | * * * * 1

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