- general polytopal classes:
- scaliform partial Stott expansions
links
| Acronym | pexhax |
| Name | partially expanded hemihexeract |
| Circumradius | sqrt(7)/2 = 1.322876 |
| Coordinates | (1/sqrt(8), 1/sqrt(8), 3/sqrt(8); 1/sqrt(8), 1/sqrt(8), 1/sqrt(8)) & all permutations of either coord. subset, all even changes of sign in either coord. subset |
| Face vector | 96, 576, 1312, 1256, 488, 64 |
| Confer |
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External links |
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Incidence matrix according to Dynkin symbol
o3o4s2x3o4s
demi( . . . . . . ) | 96 | 2 3 6 1 | 1 6 6 3 18 9 2 | 1 3 6 3 1 6 8 18 12 9 | 2 2 6 3 3 3 8 5 12 | 1 2 1 3 5
--------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
demi( . . . x . . ) | 2 | 96 * * * | 1 3 3 0 0 0 1 | 0 3 0 0 1 3 0 9 0 6 | 1 0 3 0 3 3 4 0 9 | 1 1 0 3 4
. o4s . . . | 2 | * 144 * * | 0 2 0 2 4 0 0 | 1 1 2 0 0 4 4 4 2 0 | 2 2 2 1 0 2 4 2 2 | 1 2 1 1 2
. . s 2 . s | 2 | * * 288 * | 0 0 1 0 4 2 0 | 0 0 2 1 0 0 2 4 4 2 | 0 1 2 2 1 0 2 2 4 | 0 1 1 2 2
. . . . o4s | 2 | * * * 48 | 0 0 0 0 0 6 2 | 0 0 0 3 1 0 0 0 6 6 | 0 0 0 3 3 0 0 2 6 | 0 0 1 3 2
--------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
demi( . . . x3o . ) | 3 | 3 0 0 0 | 32 * * * * * * | 0 3 0 0 1 0 0 0 0 3 | 0 0 0 0 3 3 0 0 6 | 1 0 0 3 3
. o4s2x . . | 4 | 2 2 0 0 | * 144 * * * * * | 0 1 0 0 0 2 0 2 0 0 | 1 0 1 0 0 2 2 0 2 | 1 1 0 1 2
. . s2x 2 s | 4 | 2 0 2 0 | * * 144 * * * * | 0 0 0 0 0 0 0 4 0 2 | 0 0 2 0 1 0 2 0 4 | 0 1 0 2 2
sefa( o3o4s . . . ) | 3 | 0 3 0 0 | * * * 96 * * * | 1 0 0 0 0 2 2 0 0 0 | 2 2 0 0 0 1 2 1 0 | 1 2 1 0 1
sefa( . o4s 2 . s ) | 3 | 0 1 2 0 | * * * * 576 * * | 0 0 1 0 0 0 1 1 1 0 | 0 1 1 1 0 0 1 1 1 | 0 1 1 1 1
sefa( . . s 2 o4s ) | 3 | 0 0 2 1 | * * * * * 288 * | 0 0 0 1 0 0 0 0 2 1 | 0 0 0 2 1 0 0 1 2 | 0 0 1 2 1
sefa( . . . x3o4s ) | 6 | 3 0 0 3 | * * * * * * 32 | 0 0 0 0 1 0 0 0 0 3 | 0 0 0 0 3 0 0 0 3 | 0 0 0 3 1
--------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
o3o4s . . . ♦ 4 | 0 6 0 0 | 0 0 0 4 0 0 0 | 24 * * * * * * * * * | 2 2 0 0 0 0 0 0 0 | 1 2 1 0 0
. o4s2x3o . ♦ 6 | 6 3 0 0 | 2 3 0 0 0 0 0 | * 48 * * * * * * * * | 0 0 0 0 0 2 0 0 2 | 1 0 0 1 2
. o4s 2 . s ♦ 4 | 0 2 4 0 | 0 0 0 0 4 0 0 | * * 144 * * * * * * * | 0 1 1 1 0 0 0 0 0 | 0 1 1 1 0
. . s 2 o4s ♦ 4 | 0 0 4 2 | 0 0 0 0 0 4 0 | * * * 72 * * * * * * | 0 0 0 2 1 0 0 0 0 | 0 0 1 2 0
. . . x3o4s ♦ 12 | 12 0 0 6 | 4 0 0 0 0 0 4 | * * * * 8 * * * * * | 0 0 0 0 3 0 0 0 0 | 0 0 0 3 0
sefa( o3o4s2x . . ) ♦ 6 | 3 6 0 0 | 0 3 0 2 0 0 0 | * * * * * 96 * * * * | 1 0 0 0 0 1 1 0 0 | 1 1 0 0 1
sefa( o3o4s 2 . s ) ♦ 4 | 0 3 3 0 | 0 0 0 1 3 0 0 | * * * * * * 192 * * * | 0 1 0 0 0 0 1 1 0 | 0 1 1 0 1
sefa( . o4s2x 2 s ) ♦ 6 | 3 2 4 0 | 0 1 2 0 2 0 0 | * * * * * * * 288 * * | 0 0 1 0 0 0 1 0 1 | 0 1 0 1 1
sefa( . o4s 2 o4s ) ♦ 4 | 0 1 4 1 | 0 0 0 0 2 2 0 | * * * * * * * * 288 * | 0 0 0 1 0 0 0 1 1 | 0 0 1 1 1
sefa( . . s2x3o4s ) ♦ 9 | 6 0 6 3 | 1 0 3 0 0 3 1 | * * * * * * * * * 96 | 0 0 0 0 1 0 0 0 2 | 0 0 0 2 1
--------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
o3o4s2x . . ♦ 8 | 4 12 0 0 | 0 6 0 8 0 0 0 | 2 0 0 0 0 4 0 0 0 0 | 24 * * * * * * * * | 1 1 0 0 0
o3o4s 2 . s ♦ 8 | 0 12 12 0 | 0 0 0 8 24 0 0 | 2 0 6 0 0 0 8 0 0 0 | * 24 * * * * * * * | 0 1 1 0 0
. o4s2x 2 s ♦ 8 | 4 4 8 0 | 0 2 4 0 8 0 0 | 0 0 2 0 0 0 0 4 0 0 | * * 72 * * * * * * | 0 1 0 1 0
. o4s 2 o4s ♦ 8 | 0 4 16 4 | 0 0 0 0 16 16 0 | 0 0 4 4 0 0 0 0 8 0 | * * * 36 * * * * * | 0 0 1 1 0
. . s2x3o4s ♦ 24 | 24 0 24 12 | 8 0 12 0 0 24 8 | 0 0 0 6 2 0 0 0 0 8 | * * * * 12 * * * * | 0 0 0 2 0
sefa( o3o4s2x3o . ) ♦ 9 | 9 9 0 0 | 3 9 0 3 0 0 0 | 0 3 0 0 0 3 0 0 0 0 | * * * * * 32 * * * | 1 0 0 0 1
sefa( o3o4s2x 2 s ) ♦ 8 | 4 6 6 0 | 0 3 3 2 6 0 0 | 0 0 0 0 0 1 2 3 0 0 | * * * * * * 96 * * | 0 1 0 0 1
sefa( o3o4s 2 o4s ) ♦ 5 | 0 3 6 1 | 0 0 0 1 6 3 0 | 0 0 0 0 0 0 2 0 3 0 | * * * * * * * 96 * | 0 0 1 0 1
sefa( . o4s2x3o4s ) ♦ 12 | 9 3 12 3 | 2 3 6 0 6 6 1 | 0 1 0 0 0 0 0 3 3 2 | * * * * * * * * 96 | 0 0 0 1 1
--------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------
o3o4s2x3o . ♦ 12 | 12 18 0 0 | 4 18 0 12 0 0 0 | 3 6 0 0 0 12 0 0 0 0 | 3 0 0 0 0 4 0 0 0 | 8 * * * *
o3o4s2x 2 s ♦ 16 | 8 24 24 0 | 0 12 12 16 48 0 0 | 4 0 12 0 0 8 16 24 0 0 | 2 2 6 0 0 0 8 0 0 | * 12 * * *
o3o4s 2 o4s ♦ 16 | 0 24 48 8 | 0 0 0 16 96 48 0 | 4 0 24 12 0 0 32 0 48 0 | 0 4 0 6 0 0 0 16 0 | * * 6 * *
. o4s2x3o4s ♦ 48 | 48 24 96 24 | 16 24 48 0 96 96 16 | 0 8 24 24 4 0 0 48 48 32 | 0 0 12 6 4 0 0 0 16 | * * * 6 *
sefa( o3o4s2x3o4s ) ♦ 15 | 12 9 18 3 | 3 9 9 3 18 9 1 | 0 3 0 0 0 3 6 9 9 3 | 0 0 0 0 0 1 3 3 3 | * * * * 32
starting figure: o3o4x x3o4x
xo3xx3ox xo3oo3ox&#zx → height = 0 (tegum sum of 2 bi-inverted tettuts) o.3o.3o. o.3o.3o. & | 96 | 1 2 3 6 | 2 1 6 3 9 6 18 | 1 3 6 1 9 3 12 18 8 6 | 3 2 3 12 3 5 8 6 2 | 1 3 5 1 2 ------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------ x. .. .. .. .. .. & | 2 | 48 * * * | 2 0 0 0 6 0 0 | 1 0 0 0 6 3 6 0 0 0 | 0 0 3 6 3 2 0 0 0 | 0 3 2 1 0 .. x. .. .. .. .. & | 2 | * 96 * * | 1 1 3 0 0 3 0 | 1 3 3 0 6 0 0 9 0 0 | 3 1 3 9 0 0 4 3 0 | 1 3 4 0 1 .. .. .. x. .. .. & | 2 | * * 144 * | 0 0 2 2 0 0 4 | 0 1 4 1 0 0 2 4 4 2 | 2 2 0 2 1 2 4 2 2 | 1 1 2 1 2 oo3oo3oo oo3oo3oo&#x | 2 | * * * 288 | 0 0 0 0 2 1 4 | 0 0 0 0 2 1 4 4 2 2 | 0 0 1 4 2 2 2 2 1 | 0 2 2 1 1 ------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------ x.3x. .. .. .. .. & | 6 | 3 3 0 0 | 32 * * * * * * | 1 0 0 0 3 0 0 0 0 0 | 0 0 3 3 0 0 0 0 0 | 0 3 1 0 0 .. x.3o. .. .. .. & | 3 | 0 3 0 0 | * 32 * * * * * | 1 3 0 0 3 0 0 0 0 0 | 3 0 3 6 0 0 0 0 0 | 1 3 3 0 0 .. x. .. x. .. .. & | 4 | 0 2 2 0 | * * 144 * * * * | 0 1 2 0 0 0 0 2 0 0 | 2 1 0 2 0 0 2 1 0 | 1 1 2 0 1 .. .. .. x.3o. .. & | 3 | 0 0 3 0 | * * * 96 * * * | 0 0 2 1 0 0 0 0 2 0 | 1 2 0 0 0 1 2 0 2 | 1 0 1 1 2 xo .. .. .. .. ..&#x & | 3 | 1 0 0 2 | * * * * 288 * * | 0 0 0 0 1 1 2 0 0 0 | 0 0 1 2 2 1 0 0 0 | 0 2 1 1 0 .. xx .. .. .. ..&#x | 4 | 0 2 0 2 | * * * * * 144 * | 0 0 0 0 2 0 0 4 0 0 | 0 0 1 4 0 0 2 2 0 | 0 2 2 0 1 .. .. .. xo .. ..&#x & | 3 | 0 0 1 2 | * * * * * * 576 | 0 0 0 0 0 0 1 1 1 1 | 0 0 0 1 1 1 1 1 1 | 0 1 1 1 1 ------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------ x.3x.3o. .. .. .. & ♦ 12 | 6 12 0 0 | 4 4 0 0 0 0 0 | 8 * * * * * * * * * | 0 0 3 0 0 0 0 0 0 | 0 3 0 0 0 .. x.3o. x. .. .. & ♦ 6 | 0 6 3 0 | 0 2 3 0 0 0 0 | * 48 * * * * * * * * | 2 0 0 2 0 0 0 0 0 | 1 1 2 0 0 .. x. .. x.3o. .. & ♦ 6 | 0 3 6 0 | 0 0 3 2 0 0 0 | * * 96 * * * * * * * | 1 1 0 0 0 0 1 0 0 | 1 0 1 0 1 .. .. .. x.3o.3o. & ♦ 4 | 0 0 6 0 | 0 0 0 4 0 0 0 | * * * 24 * * * * * * | 0 2 0 0 0 0 0 0 2 | 1 0 0 1 2 xo3xx .. .. .. ..&#x & ♦ 9 | 3 6 0 6 | 1 1 0 0 3 3 0 | * * * * 96 * * * * * | 0 0 1 2 0 0 0 0 0 | 0 2 1 0 0 xo .. ox .. .. ..&#x ♦ 4 | 2 0 0 4 | 0 0 0 0 4 0 0 | * * * * * 72 * * * * | 0 0 1 0 2 0 0 0 0 | 0 2 0 1 0 xo .. .. .. .. ox&#x & ♦ 4 | 1 0 1 4 | 0 0 0 0 2 0 2 | * * * * * * 288 * * * | 0 0 0 1 1 1 0 0 0 | 0 1 1 1 0 .. xx .. xo .. ..&#x & ♦ 6 | 0 3 2 4 | 0 0 1 0 0 2 2 | * * * * * * * 288 * * | 0 0 0 1 0 0 1 1 0 | 0 1 1 0 1 .. .. .. xo3oo ..&#x & ♦ 4 | 0 0 3 3 | 0 0 0 1 0 0 3 | * * * * * * * * 192 * | 0 0 0 0 0 1 1 0 1 | 0 0 1 1 1 .. .. .. xo .. ox&#x ♦ 4 | 0 0 2 4 | 0 0 0 0 0 0 4 | * * * * * * * * * 144 | 0 0 0 0 1 0 0 1 1 | 0 1 0 1 1 ------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------ .. x.3o. x.3o. .. & ♦ 9 | 0 9 9 0 | 0 3 9 3 0 0 0 | 0 3 3 0 0 0 0 0 0 0 | 32 * * * * * * * * | 1 0 1 0 0 .. x. .. x.3o.3o. & ♦ 8 | 0 4 12 0 | 0 0 6 8 0 0 0 | 0 0 4 2 0 0 0 0 0 0 | * 24 * * * * * * * | 1 0 0 0 1 xo3xx3ox .. .. ..&#x ♦ 24 | 12 24 0 24 | 8 8 0 0 24 12 0 | 2 0 0 0 8 6 0 0 0 0 | * * 12 * * * * * * | 0 2 0 0 0 xo3xx .. .. .. ox&#x & ♦ 12 | 3 9 3 12 | 1 2 3 0 6 6 6 | 0 1 0 0 2 0 3 3 0 0 | * * * 96 * * * * * | 0 1 1 0 0 xo .. ox xo .. ox&#zx ♦ 8 | 4 0 4 16 | 0 0 0 0 16 0 16 | 0 0 0 0 0 4 8 0 0 4 | * * * * 36 * * * * | 0 1 0 1 0 xo .. .. .. oo3ox&#x & ♦ 5 | 1 0 3 6 | 0 0 0 1 3 0 6 | 0 0 0 0 0 0 3 0 2 0 | * * * * * 96 * * * | 0 0 1 1 0 .. xx .. xo3oo ..&#x & ♦ 8 | 0 4 6 6 | 0 0 3 2 0 3 6 | 0 0 1 0 0 0 0 3 2 0 | * * * * * * 96 * * | 0 0 1 0 1 .. xx .. xo .. ox&#x ♦ 8 | 0 4 4 8 | 0 0 2 0 0 4 8 | 0 0 0 0 0 0 0 4 0 2 | * * * * * * * 72 * | 0 1 0 0 1 .. .. .. xo3oo3ox&#x ♦ 8 | 0 0 12 12 | 0 0 0 8 0 0 24 | 0 0 0 2 0 0 0 0 8 6 | * * * * * * * * 24 | 0 0 0 1 1 ------------------------+----+---------------+--------------------------+----------------------------------+----------------------------+------------ .. x.3o. x.3o.3o. & ♦ 12 | 0 12 18 0 | 0 4 18 12 0 0 0 | 0 6 12 3 0 0 0 0 0 0 | 4 3 0 0 0 0 0 0 0 | 8 * * * * xo3xx3ox xo .. ox&#zx ♦ 48 | 24 48 24 96 | 16 16 24 0 96 48 96 | 4 8 0 0 32 24 48 48 0 24 | 0 0 4 16 6 0 0 12 0 | * 6 * * * xo3xx .. .. oo3ox&#x & ♦ 15 | 3 12 9 18 | 1 3 9 3 9 9 18 | 0 3 3 0 3 0 9 9 6 0 | 1 0 0 3 0 3 3 0 0 | * * 32 * * xo .. ox xo3oo3ox&#zx ♦ 16 | 8 0 24 48 | 0 0 0 16 48 0 96 | 0 0 0 4 0 12 48 0 32 24 | 0 0 0 0 6 16 0 0 4 | * * * 6 * .. xx .. xo3oo3ox&#x ♦ 16 | 0 8 24 24 | 0 0 12 16 0 12 48 | 0 0 8 4 0 0 0 24 16 12 | 0 2 0 0 0 0 8 6 2 | * * * * 12
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