Acronym ..., s∞o2s4s4s
Name full snub square prismatic honeycomb

This honeycomb as a total can not be made uniform: The mere alternated faceting (here starting at grothaph) e.g. would use edges of 2 different sizes: |sefa(s4s)| = x(8,2) = k = sqrt[2+sqrt(2)] = 1.847759 and |s2s| = x(4,2) = q = sqrt(2) = 1.414214 (refering to elements of s∞o2s4s4s here).


Incidence matrix according to Dynkin symbol

s∞o2s4s4s   (N → ∞)

demi( . . . . . ) | 4N |  2  2  2  1  2  2 | 1 1  6  6  6 | 2  2 2  5
------------------+----+-------------------+--------------+----------
      s 2 s . .   |  2 | 4N  *  *  *  *  * | 0 0  2  2  0 | 1  1 0  2  q
      s 2 . s .   |  2 |  * 4N  *  *  *  * | 0 0  2  0  2 | 1  0 1  2  q
      s 2 . . s   |  2 |  *  * 4N  *  *  * | 0 0  0  2  2 | 0  1 1  2  q
      . . s 2 s   |  2 |  *  *  * 2N  *  * | 0 0  0  4  0 | 0  2 0  2  q
sefa( . . s4s . ) |  2 |  *  *  *  * 4N  * | 1 0  2  0  0 | 2  0 0  1  k
sefa( . . . s4s ) |  2 |  *  *  *  *  * 4N | 0 1  0  0  2 | 0  0 2  1  k
------------------+----+-------------------+--------------+----------
      . . s4s .   |  4 |  0  0  0  0  4  0 | N *  *  *  * | 2  0 0  0  k4o
      . . . s4s   |  4 |  0  0  0  0  0  4 | * N  *  *  * | 0  0 2  0  k4o
sefa( s 2 s4s . ) |  3 |  1  1  0  0  1  0 | * * 8N  *  * | 1  0 0  1  ok&#q
sefa( s 2 s 2 s ) |  3 |  1  0  1  1  0  0 | * *  * 8N  * | 0  1 0  1  q3o
sefa( s 2 . s4s ) |  3 |  0  1  1  0  0  1 | * *  *  * 8N | 0  0 1  1  ok&#q
------------------+----+-------------------+--------------+----------
      s 2 s4s .   |  8 |  4  4  0  0  8  0 | 2 0  8  0  0 | N  * *  *  ko4ok&#q squap variant
      s 2 s 2 s   |  4 |  2  0  2  2  0  0 | 0 0  0  4  0 | * 2N *  *  q-tet
      s 2 . s4s   |  8 |  0  4  4  0  0  8 | 0 2  0  0  8 | *  * N  *  ko4ok&#q squap variant
sefa( s∞o2s4s4s ) |  5 |  2  2  2  1  1  1 | 0 0  2  2  2 | *  * * 4N  tridpy variant

starting figure: x∞o x4x4x

s∞o2s4s4o   (N → ∞)

demi( . . . . . ) | 2N |  2  4 1  4 | 2 12  6 | 4 2  5
------------------+----+------------+---------+-------
      s 2 s . .   |  2 | 2N  * *  * | 0  4  0 | 2 0  2  q
      s 2 . s .   |  2 |  * 4N *  * | 0  2  2 | 1 1  2  q
      . . . s4o   |  2 |  *  * N  * | 0  0  4 | 0 2  2  q
sefa( . . s4s . ) |  2 |  *  * * 4N | 1  2  0 | 2 0  1  k
------------------+----+------------+---------+-------
      . . s4s .   |  4 |  0  0 0  4 | N  *  * | 2 0  0  k4o
sefa( s 2 s4s . ) |  3 |  1  1 0  1 | * 8N  * | 1 0  1  ok&#q
sefa( s 2 . s4o ) |  3 |  0  2 1  0 | *  * 4N | 0 1  1  q3o
------------------+----+------------+---------+-------
      s 2 s4s .   |  8 |  4  4 0  8 | 2  8  0 | N *  *  ko4ok&#q squap variant
      s 2 . s4o   |  4 |  0  4 2  0 | 0  0  4 | * N  *  q-tet
sefa( s∞o2s4s4o ) |  5 |  2  4 1  2 | 0  4  2 | * * 2N  tridpy variant

starting figure: x∞o x4x4o

© 2004-2021
top of page