| Acronym | ... |
| Name | 2rico (?) |
| Circumradius | sqrt(3) = 1.732051 |
| Coordinates | (sqrt(2), 1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign |
| General of army | rico |
| Colonel of regiment | rico |
| Confer |
|
Looks like a compound of 2 coincident rectified icositetrachora (rico), and indeed edges, squars, and cubes (cube) all coincide by pairs.
Incidence matrix according to Dynkin symbol
β3x4o3o
both( . . . . ) | 192 | 3 3 | 3 3 3 | 1 3 1
----------------+-----+---------+------------+---------
both( . x . . ) | 2 | 288 * | 2 1 0 | 1 2 0
sefa( β3x . . ) | 2 | * 288 | 0 1 2 | 0 2 1
----------------+-----+---------+------------+---------
both( . x4o . ) | 4 | 4 0 | 144 * * | 1 1 0
β3x . . ♦ 6 | 3 3 | * 96 * | 0 2 0
sefa( β3x4o . ) | 4 | 0 4 | * * 144 | 0 1 1
----------------+-----+---------+------------+---------
both( . x4o3o ) ♦ 8 | 12 0 | 6 0 0 | 24 * *
β3x4o . ♦ 24 | 24 24 | 6 8 6 | * 24 *
sefa( β3x4o3o ) ♦ 8 | 0 12 | 0 0 6 | * * 24
starting figure: x3x4o3o
x3β3x4o
both( . . . . ) | 192 | 1 2 1 2 | 2 1 1 2 2 1 | 1 2 1 1
----------------+-----+---------------+-------------------+-----------
both( x . . . ) | 2 | 96 * * * | 2 0 1 0 0 0 | 1 2 0 0
both( . . x . ) | 2 | * 192 * * | 1 1 0 1 0 0 | 1 1 1 0
sefa( x3β . . ) | 2 | * * 96 * | 0 0 1 0 2 0 | 0 2 0 1
sefa( . β3x . ) | 2 | * * * 192 | 0 0 0 1 1 1 | 0 1 1 1
----------------+-----+---------------+-------------------+-----------
both( x . x . ) | 4 | 2 2 0 0 | 96 * * * * * | 1 1 0 0
both( . . x4o ) | 4 | 0 4 0 0 | * 48 * * * * | 1 0 1 0
x3β . . ♦ 6 | 3 0 3 0 | * * 32 * * * | 0 2 0 0
. β3x . ♦ 6 | 0 3 0 3 | * * * 64 * * | 0 1 1 0
sefa( x3β3x . ) | 4 | 0 0 2 2 | * * * * 96 * | 0 1 0 1
sefa( . β3x4o ) | 4 | 0 0 0 4 | * * * * * 48 | 0 0 1 1
----------------+-----+---------------+-------------------+-----------
both( x . x4o ) ♦ 8 | 4 8 0 0 | 4 2 0 0 0 0 | 24 * * *
x3β3x . ♦ 24 | 12 12 12 12 | 6 0 4 4 6 0 | * 16 * *
. β3x4o ♦ 24 | 0 24 0 24 | 0 6 0 8 0 6 | * * 8 *
sefa( x3β3x4o ) ♦ 8 | 0 0 4 8 | 0 0 0 0 4 2 | * * * 24
starting figure: x3x3x4o
β3β3x4o
both( . . . . ) | 192 | 2 2 2 | 1 1 2 4 1 | 2 1 2
----------------+-----+-------------+-----------------+--------
both( . . x . ) | 2 | 192 * * | 1 0 1 1 0 | 1 1 1
sefa( s3s . . ) | 2 | * 192 * | 0 1 0 2 0 | 2 0 1
sefa( . β3x . ) | 2 | * * 192 | 0 0 1 1 1 | 1 1 1
----------------+-----+-------------+-----------------+--------
both( . . x4o ) | 4 | 4 0 0 | 48 * * * * | 0 1 1
both( s3s . . ) ♦ 3 | 0 3 0 | * 64 * * * | 2 0 0
. β3x . ♦ 6 | 3 0 3 | * * 64 * * | 1 1 0
sefa( β3β3x . ) | 4 | 1 2 1 | * * * 192 * | 1 0 1
sefa( . β3x4o ) | 4 | 0 0 4 | * * * * 48 | 0 1 1
----------------+-----+-------------+-----------------+--------
β3β3x . ♦ 24 | 12 24 12 | 0 8 4 12 0 | 16 * *
. β3x4o ♦ 24 | 24 0 24 | 6 0 8 0 6 | * 8 *
sefa( β3β3x4o ) ♦ 8 | 4 4 4 | 1 0 0 4 1 | * * 48
starting figure: x3x3x4o
x3β3x *b3x
both( . . . . ) | 192 | 1 1 1 1 1 1 | 1 1 1 1 1 1 1 1 1 | 1 1 1 1 1
-------------------+-----+-------------------+----------------------------+------------
both( x . . . ) | 2 | 96 * * * * * | 1 1 0 1 0 0 0 0 0 | 1 1 1 0 0
both( . . x . ) | 2 | * 96 * * * * | 1 0 1 0 1 0 0 0 0 | 1 1 0 1 0
both( . . . x ) | 2 | * * 96 * * * | 0 1 1 0 0 1 0 0 0 | 1 0 1 1 0
sefa( x3β . . ) | 2 | * * * 96 * * | 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1
sefa( . β3x . ) | 2 | * * * * 96 * | 0 0 0 0 1 0 1 0 1 | 0 1 0 1 1
sefa( . β . *b3x ) | 2 | * * * * * 96 | 0 0 0 0 0 1 0 1 1 | 0 0 1 1 1
-------------------+-----+-------------------+----------------------------+------------
both( x . x . ) | 4 | 2 2 0 0 0 0 | 48 * * * * * * * * | 1 1 0 0 0
both( x . . x ) | 4 | 2 0 2 0 0 0 | * 48 * * * * * * * | 1 0 1 0 0
both( . . x x ) | 4 | 0 2 2 0 0 0 | * * 48 * * * * * * | 1 0 0 1 0
x3β . . ♦ 6 | 3 0 0 3 0 0 | * * * 32 * * * * * | 0 1 1 0 0
. β3x . ♦ 6 | 0 3 0 0 3 0 | * * * * 32 * * * * | 0 1 0 1 0
. β . *b3x ♦ 6 | 0 0 3 0 0 3 | * * * * * 32 * * * | 0 0 1 1 0
sefa( x3β3x . ) | 4 | 0 0 0 2 2 0 | * * * * * * 48 * * | 0 1 0 0 1
sefa( x3β . *b3x ) | 4 | 0 0 0 2 0 2 | * * * * * * * 48 * | 0 0 1 0 1
sefa( . β3x *b3x ) | 4 | 0 0 0 0 2 2 | * * * * * * * * 48 | 0 0 0 1 1
-------------------+-----+-------------------+----------------------------+------------
both( x . x x ) ♦ 8 | 4 4 4 0 0 0 | 2 2 2 0 0 0 0 0 0 | 24 * * * *
x3β3x . ♦ 24 | 12 12 0 12 12 0 | 6 0 0 4 4 0 6 0 0 | * 8 * * *
x3β . *b3x ♦ 24 | 12 0 12 12 0 12 | 0 6 0 4 0 4 0 6 0 | * * 8 * *
. β3x *b3x ♦ 24 | 0 12 12 0 12 12 | 0 0 6 0 4 4 0 0 6 | * * * 8 *
sefa( x3β3x *b3x ) ♦ 8 | 0 0 0 4 4 4 | 0 0 0 0 0 0 2 2 2 | * * * * 24
starting figure: x3x3x *b3x
β3β3x *b3x
both( . . . . ) | 192 | 1 1 2 1 1 | 1 1 1 1 2 2 1 | 1 1 1 2
-------------------+-----+-----------------+----------------------+---------
both( . . x . ) | 2 | 96 * * * * | 1 0 1 0 1 0 0 | 1 0 1 1
both( . . . x ) | 2 | * 96 * * * | 1 0 0 1 0 1 0 | 0 1 1 1
sefa( s3s . . ) | 2 | * * 192 * * | 0 1 0 0 1 1 0 | 1 1 0 1
sefa( . β3x . ) | 2 | * * * 96 * | 0 0 1 0 1 0 1 | 1 0 1 1
sefa( . β . *b3x ) | 2 | * * * * 96 | 0 0 0 1 0 1 1 | 0 1 1 1
-------------------+-----+-----------------+----------------------+---------
both( . . x x ) | 4 | 2 2 0 0 0 | 48 * * * * * * | 0 0 1 1
both( s3s . . ) ♦ 3 | 0 0 3 0 0 | * 64 * * * * * | 1 1 0 0
. β3x . ♦ 6 | 3 0 0 3 0 | * * 32 * * * * | 1 0 1 0
. β . *b3x ♦ 6 | 3 0 0 0 3 | * * * 32 * * * | 0 1 1 0
sefa( β3β3x . ) | 4 | 1 0 2 1 0 | * * * * 96 * * | 1 0 0 1
sefa( β3β . *b3x ) | 4 | 0 1 2 0 1 | * * * * * 96 * | 0 1 0 1
sefa( . β3x *b3x ) | 4 | 0 0 0 2 2 | * * * * * * 48 | 0 0 1 1
-------------------+-----+-----------------+----------------------+---------
β3β3x . ♦ 24 | 12 0 24 12 0 | 0 8 4 0 12 0 0 | 8 * * *
β3β . x ♦ 24 | 0 12 24 0 12 | 0 8 0 4 0 12 0 | * 8 * *
. β3x *b3x ♦ 24 | 12 12 0 12 12 | 6 0 4 4 0 0 6 | * * 8 *
sefa( β3β3x *b3x ) ♦ 8 | 2 2 4 2 2 | 1 0 0 0 2 2 1 | * * * 48
starting figure: x3x3x *b3x
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