|
Acronym
|
suph
|
|
Name
|
small petated hexadecaexon,
hexicated octaexon,
expanded octaexon,
lattice A7 contact polytope (span of its roots),
equatorial cross-section of oca-first soxeb,
equatorial cross-section of roc-first rek
|
|
Circumradius
|
1
|
Inradius
wrt. hop
|
2/sqrt(7) = 0.755929
|
Inradius
wrt. hixip
|
1/sqrt(3) = 0.577350
|
Inradius
wrt. trapen
|
2/sqrt(15) = 0.516398
|
Inradius
wrt. tetdip
|
1/2 = 0.5
|
Lace city
in approx. ASCII-art
|
o h -- o3o3o3o3o3x (hop)
H S h -- x3o3o3o3o3x (staf)
H o -- x3o3o3o3o3o (dual hop)
where:
o - o3o3o3o3o (point)
h - x3o3o3o3o (hix)
S - x3o3o3o3x (scad)
H - o3o3o3o3x (dual hix)
|
|
Volume
|
143/840 = 0.170238
|
|
Surface
|
[350+42 sqrt(3)+sqrt(7)+105 sqrt(15)]/360 = 2.311264
|
|
Face vector
|
56, 336, 980, 1680, 1736, 1008, 254
|
|
Confer
|
- more general:
-
xPo3o...o3oPxQ*a
- uniform relative:
-
laq
- related segmentoexa:
-
hopastaf
- general polytopal classes:
-
Wythoffian polyexa
- analogs:
-
maximal epanded simplex eSn
|
External
links
|
|
Incidence matrix according to Dynkin symbol
x3o3o3o3o3o3x
. . . . . . . | 56 | 6 6 | 15 30 15 | 20 60 60 20 | 15 60 90 60 15 | 6 30 60 60 30 6 | 1 6 15 20 15 6 1
--------------+----+---------+-------------+-----------------+---------------------+-----------------------+-------------------
x . . . . . . | 2 | 168 * | 5 5 0 | 10 20 10 0 | 10 30 30 10 0 | 5 20 30 20 5 0 | 1 5 10 10 5 1 0
. . . . . . x | 2 | * 168 | 0 5 5 | 0 10 20 10 | 0 10 30 30 10 | 0 5 20 30 20 5 | 0 1 5 10 10 5 1
--------------+----+---------+-------------+-----------------+---------------------+-----------------------+-------------------
x3o . . . . . | 3 | 3 0 | 280 * * | 4 4 0 0 | 6 12 6 0 0 | 4 12 12 4 0 0 | 1 4 6 4 1 0 0
x . . . . . x | 4 | 2 2 | * 420 * | 0 4 4 0 | 0 6 12 6 0 | 0 4 12 12 4 0 | 0 1 4 6 4 1 0
. . . . . o3x | 3 | 0 3 | * * 280 | 0 0 4 4 | 0 0 6 12 6 | 0 0 4 12 12 4 | 0 0 1 4 6 4 1
--------------+----+---------+-------------+-----------------+---------------------+-----------------------+-------------------
x3o3o . . . . ♦ 4 | 6 0 | 4 0 0 | 280 * * * | 3 3 0 0 0 | 3 6 3 0 0 0 | 1 3 3 1 0 0 0
x3o . . . . x ♦ 6 | 6 3 | 2 3 0 | * 560 * * | 0 3 3 0 0 | 0 3 6 3 0 0 | 0 1 3 3 1 0 0
x . . . . o3x ♦ 6 | 3 6 | 0 3 2 | * * 560 * | 0 0 3 3 0 | 0 0 3 6 3 0 | 0 0 1 3 3 1 0
. . . . o3o3x ♦ 4 | 0 6 | 0 0 4 | * * * 280 | 0 0 0 3 3 | 0 0 0 3 6 3 | 0 0 0 1 3 3 1
--------------+----+---------+-------------+-----------------+---------------------+-----------------------+-------------------
x3o3o3o . . . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 0 | 168 * * * * | 2 2 0 0 0 0 | 1 2 1 0 0 0 0
x3o3o . . . x ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 | * 420 * * * | 0 2 2 0 0 0 | 0 1 2 1 0 0 0
x3o . . . o3x ♦ 9 | 9 9 | 3 9 3 | 0 3 3 0 | * * 560 * * | 0 0 2 2 0 0 | 0 0 1 2 1 0 0
x . . . o3o3x ♦ 8 | 4 12 | 0 6 8 | 0 0 4 2 | * * * 420 * | 0 0 0 2 2 0 | 0 0 0 1 2 1 0
. . . o3o3o3x ♦ 5 | 0 10 | 0 0 10 | 0 0 0 5 | * * * * 168 | 0 0 0 0 2 2 | 0 0 0 0 1 2 1
--------------+----+---------+-------------+-----------------+---------------------+-----------------------+-------------------
x3o3o3o3o . . ♦ 6 | 15 0 | 20 0 0 | 15 0 0 0 | 6 0 0 0 0 | 56 * * * * * | 1 1 0 0 0 0 0
x3o3o3o . . x ♦ 10 | 20 5 | 20 10 0 | 10 10 0 0 | 2 5 0 0 0 | * 168 * * * * | 0 1 1 0 0 0 0
x3o3o . . o3x ♦ 12 | 18 12 | 12 18 4 | 3 12 6 0 | 0 3 4 0 0 | * * 280 * * * | 0 0 1 1 0 0 0
x3o . . o3o3x ♦ 12 | 12 18 | 4 18 12 | 0 6 12 3 | 0 0 4 3 0 | * * * 280 * * | 0 0 0 1 1 0 0
x . . o3o3o3x ♦ 10 | 5 20 | 0 10 20 | 0 0 10 10 | 0 0 0 5 2 | * * * * 168 * | 0 0 0 0 1 1 0
. . o3o3o3o3x ♦ 6 | 0 15 | 0 0 20 | 0 0 0 15 | 0 0 0 0 6 | * * * * * 56 | 0 0 0 0 0 1 1
--------------+----+---------+-------------+-----------------+---------------------+-----------------------+-------------------
x3o3o3o3o3o . ♦ 7 | 21 0 | 35 0 0 | 35 0 0 0 | 21 0 0 0 0 | 7 0 0 0 0 0 | 8 * * * * * *
x3o3o3o3o . x ♦ 12 | 30 6 | 40 15 0 | 30 20 0 0 | 12 15 0 0 0 | 2 6 0 0 0 0 | * 28 * * * * *
x3o3o3o . o3x ♦ 15 | 30 15 | 30 30 5 | 15 30 10 0 | 3 15 10 0 0 | 0 3 5 0 0 0 | * * 56 * * * *
x3o3o . o3o3x ♦ 16 | 24 24 | 16 36 16 | 4 24 24 4 | 0 6 16 6 0 | 0 0 4 4 0 0 | * * * 70 * * *
x3o . o3o3o3x ♦ 15 | 15 30 | 5 30 30 | 0 10 30 15 | 0 0 10 15 3 | 0 0 0 5 3 0 | * * * * 56 * *
x . o3o3o3o3x ♦ 12 | 6 30 | 0 15 40 | 0 0 20 30 | 0 0 0 15 12 | 0 0 0 0 6 2 | * * * * * 28 *
. o3o3o3o3o3x ♦ 7 | 0 21 | 0 0 35 | 0 0 0 35 | 0 0 0 0 21 | 0 0 0 0 0 7 | * * * * * * 8
or
. . . . . . . | 56 | 12 | 30 30 | 40 120 | 30 120 90 | 12 60 120 | 2 12 30 20
-----------------+----+-----+---------+----------+-------------+-------------+-------------
x . . . . . . & | 2 | 336 | 5 5 | 10 30 | 10 40 30 | 5 25 50 | 1 6 15 10
-----------------+----+-----+---------+----------+-------------+-------------+-------------
x3o . . . . . & | 3 | 3 | 560 * | 4 4 | 6 12 6 | 4 12 16 | 1 4 7 4
x . . . . . x | 4 | 4 | * 420 | 0 8 | 0 12 12 | 0 8 24 | 0 2 8 6
-----------------+----+-----+---------+----------+-------------+-------------+-------------
x3o3o . . . . & ♦ 4 | 6 | 4 0 | 560 * | 3 3 0 | 3 6 3 | 1 3 3 1
x3o . . . . x & ♦ 6 | 9 | 2 3 | * 1120 | 0 3 3 | 0 3 9 | 0 1 4 3
-----------------+----+-----+---------+----------+-------------+-------------+-------------
x3o3o3o . . . & ♦ 5 | 10 | 10 0 | 5 0 | 336 * * | 2 2 0 | 1 2 1 0
x3o3o . . . x & ♦ 8 | 16 | 8 6 | 2 4 | * 840 * | 0 2 2 | 0 1 2 1
x3o . . . o3x ♦ 9 | 18 | 6 9 | 0 6 | * * 560 | 0 0 4 | 0 0 2 2
-----------------+----+-----+---------+----------+-------------+-------------+-------------
x3o3o3o3o . . & ♦ 6 | 15 | 20 0 | 15 0 | 6 0 0 | 112 * * | 1 1 0 0
x3o3o3o . . x & ♦ 10 | 25 | 20 10 | 10 10 | 2 5 0 | * 336 * | 0 1 1 0
x3o3o . . o3x & ♦ 12 | 30 | 16 18 | 3 18 | 0 3 4 | * * 560 | 0 0 1 1
-----------------+----+-----+---------+----------+-------------+-------------+-------------
x3o3o3o3o3o . & ♦ 7 | 21 | 35 0 | 35 0 | 21 0 0 | 7 0 0 | 16 * * *
x3o3o3o3o . x & ♦ 12 | 36 | 40 15 | 30 20 | 12 15 0 | 2 6 0 | * 56 * *
x3o3o3o . o3x & ♦ 15 | 45 | 35 30 | 15 40 | 3 15 10 | 0 3 5 | * * 112 *
x3o3o . o3o3x ♦ 16 | 48 | 32 36 | 8 24 | 0 12 16 | 0 0 8 | * * * 70
xxo3ooo3ooo3ooo3ooo3oxx&#xt → both heights = 2/sqrt(7) = 0.755929
(hop || pseudo staf || dual hop)
...