| Acronym | icou |
| Name |
icositetrachoron-based ursateron, ico-based ursulate, vertex figure of s3s4o3o4o3o |
| Circumradius | sqrt[(13+5 sqrt(5))/8] = 1.738546 |
| Face vector | 144, 600, 720, 312, 50 |
| Confer |
|
Incidence matrix according to Dynkin symbol
ofx3xoo4ooo3ooo&#xt → height(1,2) = sqrt[sqrt(5)-2] = 0.485868
height(2,3) = sqrt[(sqrt(5)-1)/2] = 0.786151
(rico || pseudo f-ico || ico)
o..3o..4o..3o.. | 96 * * | 6 2 0 0 | 3 6 1 6 0 | 3 2 3 6 0 | 1 3 2 0
.o.3.o.4.o.3.o. | * 24 * | 0 8 1 0 | 0 0 8 12 0 | 0 0 12 6 0 | 0 6 1 0
..o3..o4..o3..o | * * 24 | 0 0 1 8 | 0 0 8 0 12 | 0 0 12 0 6 | 0 6 0 1
--------------------+----------+---------------+------------------+-----------------+----------
... x.. ... ... | 2 0 0 | 288 * * * | 1 2 0 1 0 | 2 1 1 2 0 | 1 2 1 0
oo.3oo.4oo.3oo.&#x | 1 1 0 | * 192 * * | 0 0 1 3 0 | 0 0 3 3 0 | 0 3 1 0
.oo3.oo4.oo3.oo&#x | 0 1 1 | * * 24 * ♦ 0 0 8 0 0 | 0 0 12 0 0 | 0 6 0 0
..x ... ... ... | 0 0 2 | * * * 96 | 0 0 1 0 3 | 0 0 3 0 3 | 0 3 0 1
--------------------+----------+---------------+------------------+-----------------+----------
o..3x.. ... ... | 3 0 0 | 3 0 0 0 | 96 * * * * | 2 0 1 0 0 | 1 2 0 0
... x..4o.. ... | 4 0 0 | 4 0 0 0 | * 144 * * * | 1 1 0 1 0 | 1 1 1 0
ofx ... ... ...&#xt | 1 2 2 | 0 2 2 1 | * * 96 * * | 0 0 3 0 0 | 0 3 0 0
... xo. ... ...&#x | 2 1 0 | 1 2 0 0 | * * * 288 * | 0 0 1 2 0 | 0 2 1 0
..x3..o ... ... | 0 0 3 | 0 0 0 3 | * * * * 96 | 0 0 1 0 2 | 0 2 0 1
--------------------+----------+---------------+------------------+-----------------+----------
o..3x..4o.. ... ♦ 12 0 0 | 24 0 0 0 | 8 6 0 0 0 | 24 * * * * | 1 1 0 0
... x..4o..3o.. ♦ 8 0 0 | 12 0 0 0 | 0 6 0 0 0 | * 24 * * * | 1 0 1 0
ofx3xoo ... ...&#xt ♦ 3 3 3 | 3 6 3 3 | 1 0 3 3 1 | * * 96 * * | 0 2 0 0
... xo.4oo. ...&#x ♦ 4 1 0 | 4 4 0 0 | 0 1 0 4 0 | * * * 144 * | 0 1 1 0
..x3..o4..o ... ♦ 0 0 6 | 0 0 0 12 | 0 0 0 0 8 | * * * * 24 | 0 1 0 1
--------------------+----------+---------------+------------------+-----------------+----------
o..3x..4o..3o.. ♦ 96 0 0 | 288 0 0 0 | 96 144 0 0 0 | 24 24 0 0 0 | 1 * * *
ofx3xoo4ooo ...&#xt ♦ 12 6 6 | 24 24 6 12 | 8 6 12 24 8 | 1 0 8 6 1 | * 24 * *
... xo.4oo.3oo.&#x ♦ 8 1 0 | 12 8 0 0 | 0 6 0 12 0 | 0 1 0 6 0 | * * 24 *
..x3..o4..o3..o ♦ 0 0 24 | 0 0 0 96 | 0 0 0 0 96 | 0 0 0 0 24 | * * * 1
xoo3ofx3xoo4ooo&#xt → height(1,2) = sqrt[sqrt(5)-2] = 0.485868
height(2,3) = sqrt[(sqrt(5)-1)/2] = 0.786151
(rico || pseudo f-ico || ico)
o..3o..3o..4o.. | 96 * * | 2 4 2 0 0 | 1 4 2 2 2 1 4 0 0 | 2 2 1 1 4 2 2 0 0 | 1 2 2 1 0
.o.3.o.3.o.4.o. | * 24 * | 0 0 8 1 0 | 0 0 0 0 4 8 8 0 0 | 0 0 0 4 4 8 2 0 0 | 0 4 1 2 0
..o3..o3..o4..o | * * 24 | 0 0 0 1 8 | 0 0 0 0 0 8 0 4 8 | 0 0 0 4 0 8 0 4 2 | 0 4 0 2 1
--------------------+----------+------------------+-----------------------------+--------------------------+------------
x.. ... ... ... | 2 0 0 | 96 * * * * | 1 2 0 0 1 0 0 0 0 | 2 1 0 1 2 0 0 0 0 | 1 2 1 0 0
... ... x.. ... | 2 0 0 | * 192 * * * | 0 1 1 1 0 0 1 0 0 | 1 1 1 0 1 1 1 0 0 | 1 1 1 1 0
oo.3oo.3oo.4oo.&#x | 1 1 0 | * * 192 * * | 0 0 0 0 1 1 2 0 0 | 0 0 0 1 2 2 1 0 0 | 0 2 1 1 0
.oo3.oo3.oo4.oo&#x | 0 1 1 | * * * 24 * ♦ 0 0 0 0 0 8 0 0 0 | 0 0 0 4 0 8 0 0 0 | 0 4 0 2 0
... ..x ... ... | 0 0 2 | * * * * 96 | 0 0 0 0 0 1 0 1 2 | 0 0 0 1 0 2 0 2 1 | 0 2 0 1 1
--------------------+----------+------------------+-----------------------------+--------------------------+------------
x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 | 32 * * * * * * * * | 2 0 0 1 0 0 0 0 0 | 1 2 0 0 0
x.. ... x.. ... | 4 0 0 | 2 2 0 0 0 | * 96 * * * * * * * | 1 1 0 0 1 0 0 0 0 | 1 1 1 0 0
... o..3x.. ... | 3 0 0 | 0 3 0 0 0 | * * 64 * * * * * * | 1 0 1 0 0 1 0 0 0 | 1 1 0 1 0
... ... x..4o.. | 4 0 0 | 0 4 0 0 0 | * * * 48 * * * * * | 0 1 1 0 0 0 1 0 0 | 1 0 1 1 0
xo. ... ... ...&#x | 2 1 0 | 1 0 2 0 0 | * * * * 96 * * * * | 0 0 0 1 2 0 0 0 0 | 0 2 1 0 0
... ofx ... ...&#xt | 1 2 2 | 0 0 2 2 1 | * * * * * 96 * * * | 0 0 0 1 0 2 0 0 0 | 0 2 0 1 0
... ... xo. ...&#x | 2 1 0 | 0 1 2 0 0 | * * * * * * 192 * * | 0 0 0 0 1 1 1 0 0 | 0 1 1 1 0
..o3..x ... ... | 0 0 3 | 0 0 0 0 3 | * * * * * * * 32 * | 0 0 0 1 0 0 0 2 0 | 0 2 0 0 1
... ..x3..o ... | 0 0 3 | 0 0 0 0 3 | * * * * * * * * 64 | 0 0 0 0 0 1 0 1 1 | 0 1 0 1 1
--------------------+----------+------------------+-----------------------------+--------------------------+------------
x..3o..3x.. ... ♦ 12 0 0 | 12 12 0 0 0 | 4 6 4 0 0 0 0 0 0 | 16 * * * * * * * * | 1 1 0 0 0
x.. ... x..4o.. ♦ 8 0 0 | 4 8 0 0 0 | 0 4 0 2 0 0 0 0 0 | * 24 * * * * * * * | 1 0 1 0 0
... o..3x..4o.. ♦ 12 0 0 | 0 24 0 0 0 | 0 0 8 6 0 0 0 0 0 | * * 8 * * * * * * | 1 0 0 1 0
xoo3ofx ... ...&#xt ♦ 3 3 3 | 3 0 6 3 3 | 1 0 0 0 3 3 0 1 0 | * * * 32 * * * * * | 0 2 0 0 0
xo. ... xo. ...&#x ♦ 4 1 0 | 2 2 4 0 0 | 0 1 0 0 2 0 2 0 0 | * * * * 96 * * * * | 0 1 1 0 0
... ofx3xoo ...&#xt ♦ 3 3 3 | 0 3 6 3 3 | 0 0 1 0 0 3 3 0 1 | * * * * * 64 * * * | 0 1 0 1 0
... ... xo.4oo.&#x ♦ 4 1 0 | 0 4 4 0 0 | 0 0 0 1 0 0 4 0 0 | * * * * * * 48 * * | 0 0 1 1 0
..o3..x3..o ... ♦ 0 0 6 | 0 0 0 0 12 | 0 0 0 0 0 0 0 4 4 | * * * * * * * 16 * | 0 1 0 0 1
... ..x3..o4..o ♦ 0 0 6 | 0 0 0 0 12 | 0 0 0 0 0 0 0 0 8 | * * * * * * * * 8 | 0 0 0 1 1
--------------------+----------+------------------+-----------------------------+--------------------------+------------
x..3o..3x..4o.. ♦ 96 0 0 | 96 192 0 0 0 | 32 96 64 48 0 0 0 0 0 | 16 24 8 0 0 0 0 0 0 | 1 * * * *
xoo3ofx3xoo ...&#xt ♦ 12 6 6 | 12 12 24 6 12 | 4 6 4 0 12 12 12 4 4 | 1 0 0 4 6 4 0 1 0 | * 16 * * *
xo. ... xo.4oo.&#x ♦ 8 1 0 | 4 8 8 0 0 | 0 4 0 2 4 0 8 0 0 | 0 1 0 0 4 0 2 0 0 | * * 24 * *
... ofx3xoo4ooo&#xt ♦ 12 6 6 | 0 24 24 6 12 | 0 0 8 6 0 12 24 0 8 | 0 0 1 0 0 8 6 0 1 | * * * 8 *
..o3..x3..o4..o ♦ 0 0 24 | 0 0 0 0 96 | 0 0 0 0 0 0 0 32 64 | 0 0 0 0 0 0 0 16 8 | * * * * 1
xoo3ofx3xoo *b3xoo&#xt → height(1,2) = sqrt[sqrt(5)-2] = 0.485868
height(2,3) = sqrt[(sqrt(5)-1)/2] = 0.786151
(rico || pseudo f-ico || ico)
o..3o..3o.. *b3o.. | 96 * * | 2 2 2 2 0 0 | 1 2 2 1 2 1 2 1 2 2 0 0 0 | 1 1 2 1 1 2 2 1 1 2 0 0 0 | 1 1 1 2 1 0
.o.3.o.3.o. *b3.o. | * 24 * | 0 0 0 8 1 0 | 0 0 0 0 0 0 4 8 4 4 0 0 0 | 0 0 0 0 4 2 2 4 4 2 0 0 0 | 0 2 2 1 2 0
..o3..o3..o *b3..o | * * 24 | 0 0 0 0 1 8 | 0 0 0 0 0 0 0 8 0 0 4 4 4 | 0 0 0 0 4 0 0 4 4 0 2 2 2 | 0 2 2 0 2 1
-----------------------+----------+--------------------+----------------------------------------+----------------------------------+-------------
x.. ... ... ... | 2 0 0 | 96 * * * * * | 1 1 1 0 0 0 1 0 0 0 0 0 0 | 1 1 1 0 1 1 1 0 0 0 0 0 0 | 1 1 1 1 0 0
... ... x.. ... | 2 0 0 | * 96 * * * * | 0 1 0 1 1 0 0 0 1 0 0 0 0 | 1 0 1 1 0 1 0 1 0 1 0 0 0 | 1 1 0 1 1 0
... ... ... x.. | 2 0 0 | * * 96 * * * | 0 0 1 0 1 1 0 0 0 1 0 0 0 | 0 1 1 1 0 0 1 0 1 1 0 0 0 | 1 0 1 1 1 0
oo.3oo.3oo. *b3oo.&#x | 1 1 0 | * * * 192 * * | 0 0 0 0 0 0 1 1 1 1 0 0 0 | 0 0 0 0 1 1 1 1 1 1 0 0 0 | 0 1 1 1 1 0
.oo3.oo3.oo *b3.oo&#x | 0 1 1 | * * * * 24 * ♦ 0 0 0 0 0 0 0 8 0 0 0 0 0 | 0 0 0 0 4 0 0 4 4 0 0 0 0 | 0 2 2 0 2 0
... ..x ... ... | 0 0 2 | * * * * * 96 | 0 0 0 0 0 0 0 1 0 0 1 1 1 | 0 0 0 0 1 0 0 1 1 0 1 1 1 | 0 1 1 0 1 1
-----------------------+----------+--------------------+----------------------------------------+----------------------------------+-------------
x..3o.. ... ... | 3 0 0 | 3 0 0 0 0 0 | 32 * * * * * * * * * * * * | 1 1 0 0 1 0 0 0 0 0 0 0 0 | 1 1 1 0 0 0
x.. ... x.. ... | 4 0 0 | 2 2 0 0 0 0 | * 48 * * * * * * * * * * * | 1 0 1 0 0 1 0 0 0 0 0 0 0 | 1 1 0 1 0 0
x.. ... ... x.. | 4 0 0 | 2 0 2 0 0 0 | * * 48 * * * * * * * * * * | 0 1 1 0 0 0 1 0 0 0 0 0 0 | 1 0 1 1 0 0
... o..3x.. ... | 3 0 0 | 0 3 0 0 0 0 | * * * 32 * * * * * * * * * | 1 0 0 1 0 0 0 1 0 0 0 0 0 | 1 1 0 0 1 0
... ... x.. x.. | 4 0 0 | 0 2 2 0 0 0 | * * * * 48 * * * * * * * * | 0 0 1 1 0 0 0 0 0 1 0 0 0 | 1 0 0 1 1 0
... o.. ... *b3x.. | 3 0 0 | 0 0 3 0 0 0 | * * * * * 32 * * * * * * * | 0 1 0 1 0 0 0 0 1 0 0 0 0 | 1 0 1 0 1 0
xo. ... ... ...&#x | 2 1 0 | 1 0 0 2 0 0 | * * * * * * 96 * * * * * * | 0 0 0 0 1 1 1 0 0 0 0 0 0 | 0 1 1 1 0 0
... ofx ... ...&#xt | 1 2 2 | 0 0 0 2 2 1 | * * * * * * * 96 * * * * * | 0 0 0 0 1 0 0 1 1 0 0 0 0 | 0 1 1 0 1 0
... ... xo. ...&#x | 2 1 0 | 0 1 0 2 0 0 | * * * * * * * * 96 * * * * | 0 0 0 0 0 1 0 1 0 1 0 0 0 | 0 1 0 1 1 0
... ... ... xo.&#x | 2 1 0 | 0 0 1 2 0 0 | * * * * * * * * * 96 * * * | 0 0 0 0 0 0 1 0 1 1 0 0 0 | 0 0 1 1 1 0
..o3..x ... ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * 32 * * | 0 0 0 0 1 0 0 0 0 0 1 1 0 | 0 1 1 0 0 1
... ..x3..o ... | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * * 32 * | 0 0 0 0 0 0 0 1 0 0 1 0 1 | 0 1 0 0 1 1
... ..x ... *b3..o | 0 0 3 | 0 0 0 0 0 3 | * * * * * * * * * * * * 32 | 0 0 0 0 0 0 0 0 1 0 0 1 1 | 0 0 1 0 1 1
-----------------------+----------+--------------------+----------------------------------------+----------------------------------+-------------
x..3o..3x.. ... ♦ 12 0 0 | 12 12 0 0 0 0 | 4 6 0 4 0 0 0 0 0 0 0 0 0 | 8 * * * * * * * * * * * * | 1 1 0 0 0 0
x..3o.. ... *b3x.. ♦ 12 0 0 | 12 0 12 0 0 0 | 4 0 6 0 0 4 0 0 0 0 0 0 0 | * 8 * * * * * * * * * * * | 1 0 1 0 0 0
x.. ... x.. x.. ♦ 8 0 0 | 4 4 4 0 0 0 | 0 2 2 0 2 0 0 0 0 0 0 0 0 | * * 24 * * * * * * * * * * | 1 0 0 1 0 0
... o..3x.. *b3x.. ♦ 12 0 0 | 0 12 12 0 0 0 | 0 0 0 4 6 4 0 0 0 0 0 0 0 | * * * 8 * * * * * * * * * | 1 0 0 0 1 0
xoo3ofx ... ...&#xt ♦ 3 3 3 | 3 0 0 6 3 3 | 1 0 0 0 0 0 3 3 0 0 1 0 0 | * * * * 32 * * * * * * * * | 0 1 1 0 0 0
xo. ... xo. ...&#x ♦ 4 1 0 | 2 2 0 4 0 0 | 0 1 0 0 0 0 2 0 2 0 0 0 0 | * * * * * 48 * * * * * * * | 0 1 0 1 0 0
xo. ... ... xo.&#x ♦ 4 1 0 | 2 0 2 4 0 0 | 0 0 1 0 0 0 2 0 0 2 0 0 0 | * * * * * * 48 * * * * * * | 0 0 1 1 0 0
... ofx3xoo ...&#xt ♦ 3 3 3 | 0 3 0 6 3 3 | 0 0 0 1 0 0 0 3 3 0 0 1 0 | * * * * * * * 32 * * * * * | 0 1 0 0 1 0
... ofx ... *b3xoo&#xt ♦ 3 3 3 | 0 0 3 6 3 3 | 0 0 0 0 0 1 0 3 0 3 0 0 1 | * * * * * * * * 32 * * * * | 0 0 1 0 1 0
... ... xo. xo.&#x ♦ 4 1 0 | 0 2 2 4 0 0 | 0 0 0 0 1 0 0 0 2 2 0 0 0 | * * * * * * * * * 48 * * * | 0 0 0 1 1 0
..o3..x3..o ... ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 4 4 0 | * * * * * * * * * * 8 * * | 0 1 0 0 0 1
..o3..x ... *b3..o ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 4 0 4 | * * * * * * * * * * * 8 * | 0 0 1 0 0 1
... ..x3..o *b3..o ♦ 0 0 6 | 0 0 0 0 0 12 | 0 0 0 0 0 0 0 0 0 0 0 4 4 | * * * * * * * * * * * * 8 | 0 0 0 0 1 1
-----------------------+----------+--------------------+----------------------------------------+----------------------------------+-------------
x..3o..3x.. *b3x.. ♦ 96 0 0 | 96 96 96 0 0 0 | 32 48 48 32 48 32 0 0 0 0 0 0 0 | 8 8 24 8 0 0 0 0 0 0 0 0 0 | 1 * * * * *
xoo3ofx3xoo ...&#xt ♦ 12 6 6 | 12 12 0 24 6 12 | 4 6 0 4 0 0 12 12 12 0 4 4 0 | 1 0 0 0 4 6 0 4 0 0 1 0 0 | * 8 * * * *
xoo3ofx ... *b3xoo&#xt ♦ 12 6 6 | 12 0 12 24 6 12 | 4 0 6 0 0 4 12 12 0 12 4 0 4 | 0 1 0 0 4 0 6 0 4 0 0 1 0 | * * 8 * * *
xo. ... xo. xo.&#x ♦ 8 1 0 | 4 4 4 8 0 0 | 0 2 2 0 2 0 4 0 4 4 0 0 0 | 0 0 1 0 0 2 2 0 0 2 0 0 0 | * * * 24 * *
... ofx3xoo *b3xoo&#xt ♦ 12 6 6 | 0 12 12 24 6 12 | 0 0 0 4 6 4 0 12 12 12 0 4 4 | 0 0 0 1 0 0 0 4 4 6 0 0 1 | * * * * 8 *
..o3..x3..o *b3..o ♦ 0 0 24 | 0 0 0 0 0 96 | 0 0 0 0 0 0 0 0 0 0 32 32 32 | 0 0 0 0 0 0 0 0 0 0 8 8 8 | * * * * * 1
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