Acronym | ... |
Name | 2srahi (?) |
Circumradius | sqrt[23+10 sqrt(5)] = 6.735034 |
General of army | srahi |
Colonel of regiment | srahi |
Confer |
|
Looks like a compound of 2 coincident small rhombated hecatonicosachora (srahi), and indeed all but the Grünbaumian elements coincide by pairs. It comes in different types depending on which cells are Grünbaumian: type A uses all but the small rhombicosidodecahedra (srid) as Grünbaumian cells, while type B uses all but the triangular prisms (trip) as such. Type B even splits according to the used version of the Grünbaumian doubly covered small rhombicosidodecahedral cells (2srid): in type B1 the small rhombicosidodecahedral pentagons will be replaced by {10/2}, in type B2 they remain as pairs of coincident {5}.
Incidence matrix according to Dynkin symbol
β3x3o5x (type A) both( . . . . ) | 7200 | 2 2 2 | 1 2 1 2 1 2 | 1 1 2 1 ----------------+------+----------------+-------------------------------+----------------- both( . x . . ) | 2 | 7200 * * | 1 1 0 1 0 0 | 1 1 1 0 both( . . . x ) | 2 | * 7200 * | 0 1 1 0 0 1 | 1 0 1 1 sefa( β3x . . ) | 2 | * * 7200 | 0 0 0 1 1 1 | 0 1 1 1 ----------------+------+----------------+-------------------------------+----------------- both( . x3o . ) | 3 | 3 0 0 | 2400 * * * * * | 1 1 0 0 both( . x . x ) | 4 | 2 2 0 | * 3600 * * * * | 1 0 1 0 both( . . o5x ) | 5 | 0 5 0 | * * 1440 * * * | 1 0 0 1 β3x . . ♦ 6 | 3 0 3 | * * * 2400 * * | 0 1 1 0 sefa( β3x3o . ) | 3 | 0 0 3 | * * * * 2400 * | 0 1 0 1 sefa( β3x 2 x ) | 4 | 0 2 2 | * * * * * 3600 | 0 0 1 1 ----------------+------+----------------+-------------------------------+----------------- both( . x3o5x ) ♦ 60 | 60 60 0 | 20 30 12 0 0 0 | 120 * * * β3xo3 . ♦ 12 | 12 0 12 | 4 0 0 4 4 0 | * 600 * * β3x 2 x ♦ 12 | 6 6 6 | 0 3 0 2 0 3 | * * 1200 * sefa( β3x3o5x ) ♦ 60 | 0 60 60 | 0 0 12 0 20 30 | * * * 120 starting figure: x3x3o5x
o3x3β5x (type B1) both( . . . . ) | 7200 | 2 1 2 1 | 1 2 2 1 1 2 | 1 1 2 1 ----------------+------+---------------------+------------------------------+------------------ both( . x . . ) | 2 | 7200 * * * | 1 1 1 0 0 0 | 1 1 1 0 both( . . . x ) | 2 | * 3600 * * | 0 2 0 1 0 0 | 1 0 2 0 sefa( . x3β . ) | 2 | * * 7200 * | 0 0 1 0 1 1 | 0 1 1 1 sefa( . . β5x ) | 2 | * * * 3600 | 0 0 0 1 0 2 | 0 0 2 1 ----------------+------+---------------------+------------------------------+------------------ both( o3x . . ) | 3 | 3 0 0 0 | 2400 * * * * * | 1 1 0 0 both( . x . x ) | 4 | 2 2 0 0 | * 3600 * * * * | 1 0 1 0 . x3β . ♦ 6 | 3 0 3 0 | * * 2400 * * * | 0 1 1 0 . . β5x ♦ 10 | 0 5 0 5 | * * * 720 * * | 0 0 2 0 sefa( o3x3β . ) | 3 | 0 0 3 0 | * * * * 2400 * | 0 1 0 1 sefa( . x3β5x ) | 4 | 0 0 2 2 | * * * * * 3600 | 0 0 1 1 ----------------+------+---------------------+------------------------------+------------------ both( o3x . x ) ♦ 6 | 6 3 0 0 | 2 3 0 0 0 0 | 1200 * * * o3x3β . ♦ 12 | 12 0 12 0 | 4 0 4 0 4 0 | * 600 * * . x3β5x ♦ 120 | 60 60 60 60 | 0 30 20 12 0 30 | * * 120 * sefa( o3x3β5x ) ♦ 6 | 0 0 6 3 | 0 0 0 0 2 3 | * * * 1200 starting figure: o3x3x5x
o3x3β5β (type B2) both( . . . . ) | 7200 | 2 2 2 | 1 2 1 1 4 | 1 2 2 ----------------+------+----------------+--------------------------+------------- both( . x . . ) | 2 | 7200 * * | 1 1 0 0 1 | 1 1 1 sefa( . x3β . ) | 2 | * 7200 * | 0 1 0 1 1 | 1 1 1 sefa( . . s5s ) | 2 | * * 7200 | 0 0 1 0 2 | 0 2 1 ----------------+------+----------------+--------------------------+------------- both( o3x . . ) | 3 | 3 0 0 | 2400 * * * * | 1 0 1 . x3β . ♦ 6 | 3 3 0 | * 2400 * * * | 1 1 0 both( . . s5s ) ♦ 5 | 0 0 5 | * * 1440 * * | 0 2 0 sefa( o3x3β . ) | 3 | 0 3 0 | * * * 2400 * | 1 0 1 sefa( . x3β5β ) | 4 | 1 1 2 | * * * * 7200 | 0 1 1 ----------------+------+----------------+--------------------------+------------- o3x3β . ♦ 12 | 12 12 0 | 4 4 0 4 0 | 600 * * . x3β5β ♦ 120 | 60 60 120 | 0 20 24 0 60 | * 120 * sefa( o3x3β5β ) ♦ 6 | 3 3 3 | 1 0 0 1 3 | * * 2400 starting figure: o3x3x5x
© 2004-2024 | top of page |