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Acronym
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octu
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Name
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axially-octahedral ursachoron ofx3xoo4ooo&#xt,
oct-based ursulate,
vertex figure of s3s4o3o4o
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 ©
 ©
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Circumradius
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sqrt[3+sqrt(5)]/2 = 1.144123
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Inradius
wrt. oct
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sqrt[1+sqrt(5)]/2 = 0.899454
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Inradius
wrt. squippy
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sqrt[1+sqrt(5)]/2 = 0.899454
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Inradius
wrt. teddi
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sqrt[(1+sqrt(5))/8] = 0.636010
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Inradius
wrt. co
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sqrt[sqrt(5)-1]/2 = 0.555893
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Coordinates
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(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)
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(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)
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(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
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Face vector
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24, 66, 58, 16
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Confer
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- related CRFs:
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tetu
iku
xoBo3ofox3xooo&#xt
- general polytopal classes:
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ursatopes
bistratic lace towers
- analogs:
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ursatope oUn
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External
links
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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