Acronym | hept | ||||||||||||||||||||||||||||
Name |
hepteract, tetradecaexon, 7D measure-polytope (γ7), geozett(id) | ||||||||||||||||||||||||||||
|,>,O device | line prism prism prism prism prism prism = ||||||| | ||||||||||||||||||||||||||||
Circumradius | sqrt(7)/2 = 1.322876 | ||||||||||||||||||||||||||||
Inradius | 1/2 | ||||||||||||||||||||||||||||
Vertex layers |
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Coordinates | (1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2) & all changes of sign | ||||||||||||||||||||||||||||
Volume | 1 | ||||||||||||||||||||||||||||
Surface | 14 | ||||||||||||||||||||||||||||
Rel. Roundness | π3/840 = 3.691223 % | ||||||||||||||||||||||||||||
Dual | zee | ||||||||||||||||||||||||||||
Dihedral angles
(at margins) | |||||||||||||||||||||||||||||
Face vector | 128, 448, 672, 560, 280, 84, 14 | ||||||||||||||||||||||||||||
Confer |
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External links |
Its equatorial cross-section in vertex first orientation is not a vertex layer. Even so it can be determined as 1/q-fe (cf. truncation series).
Incidence matrix according to Dynkin symbol
o3o3o3o3o3o4x . . . . . . . | 128 ♦ 7 | 21 | 35 | 35 | 21 | 7 --------------+-----+-----+-----+-----+-----+----+--- . . . . . . x | 2 | 448 ♦ 6 | 15 | 20 | 15 | 6 --------------+-----+-----+-----+-----+-----+----+--- . . . . . o4x | 4 | 4 | 672 ♦ 5 | 10 | 10 | 5 --------------+-----+-----+-----+-----+-----+----+--- . . . . o3o4x ♦ 8 | 12 | 6 | 560 ♦ 4 | 6 | 4 --------------+-----+-----+-----+-----+-----+----+--- . . . o3o3o4x ♦ 16 | 32 | 24 | 8 | 280 | 3 | 3 --------------+-----+-----+-----+-----+-----+----+--- . . o3o3o3o4x ♦ 32 | 80 | 80 | 40 | 10 | 84 | 2 --------------+-----+-----+-----+-----+-----+----+--- . o3o3o3o3o4x ♦ 64 | 192 | 240 | 160 | 60 | 12 | 14 snubbed forms: o3o3o3o3o3o4s
o3o3o3o3o3o4/3x . . . . . . . | 128 ♦ 7 | 21 | 35 | 35 | 21 | 7 ----------------+-----+-----+-----+-----+-----+----+--- . . . . . . x | 2 | 448 ♦ 6 | 15 | 20 | 15 | 6 ----------------+-----+-----+-----+-----+-----+----+--- . . . . . o4/3x | 4 | 4 | 672 ♦ 5 | 10 | 10 | 5 ----------------+-----+-----+-----+-----+-----+----+--- . . . . o3o4/3x ♦ 8 | 12 | 6 | 560 ♦ 4 | 6 | 4 ----------------+-----+-----+-----+-----+-----+----+--- . . . o3o3o4/3x ♦ 16 | 32 | 24 | 8 | 280 | 3 | 3 ----------------+-----+-----+-----+-----+-----+----+--- . . o3o3o3o4/3x ♦ 32 | 80 | 80 | 40 | 10 | 84 | 2 ----------------+-----+-----+-----+-----+-----+----+--- . o3o3o3o3o4/3x ♦ 64 | 192 | 240 | 160 | 60 | 12 | 14
x o3o3o3o3o4x . . . . . . . | 128 ♦ 1 6 | 6 15 | 15 20 | 20 15 | 15 6 | 6 1 --------------+-----+--------+---------+---------+---------+-------+----- x . . . . . . | 2 | 64 * ♦ 6 0 | 15 0 | 20 0 | 15 0 | 6 0 . . . . . . x | 2 | * 384 ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 --------------+-----+--------+---------+---------+---------+-------+----- x . . . . . x | 4 | 2 2 | 192 * ♦ 5 0 | 10 0 | 10 0 | 5 0 . . . . . o4x | 4 | 0 4 | * 480 ♦ 1 4 | 4 6 | 6 4 | 4 1 --------------+-----+--------+---------+---------+---------+-------+----- x . . . . o4x ♦ 8 | 4 8 | 4 2 | 240 * ♦ 4 0 | 6 0 | 4 0 . . . . o3o4x ♦ 8 | 0 12 | 0 6 | * 320 ♦ 1 3 | 3 3 | 3 1 --------------+-----+--------+---------+---------+---------+-------+----- x . . . o3o4x ♦ 16 | 8 24 | 12 12 | 6 2 | 160 * | 3 0 | 3 0 . . . o3o3o4x ♦ 16 | 0 32 | 0 24 | 0 8 | * 120 | 1 2 | 2 1 --------------+-----+--------+---------+---------+---------+-------+----- x . . o3o3o4x ♦ 32 | 16 64 | 32 48 | 24 16 | 8 2 | 60 * | 2 0 . . o3o3o3o4x ♦ 32 | 0 80 | 0 80 | 0 40 | 0 10 | * 24 | 1 1 --------------+-----+--------+---------+---------+---------+-------+----- x . o3o3o3o4x ♦ 64 | 32 160 | 80 160 | 80 80 | 40 20 | 10 2 | 12 * . o3o3o3o3o4x ♦ 64 | 0 192 | 0 240 | 0 160 | 0 60 | 0 12 | * 2
x o3o3o3o3o4/3x . . . . . . . | 128 ♦ 1 6 | 6 15 | 15 20 | 20 15 | 15 6 | 6 1 ----------------+-----+--------+---------+---------+---------+-------+----- x . . . . . . | 2 | 64 * ♦ 6 0 | 15 0 | 20 0 | 15 0 | 6 0 . . . . . . x | 2 | * 384 ♦ 1 5 | 5 10 | 10 10 | 10 5 | 5 1 ----------------+-----+--------+---------+---------+---------+-------+----- x . . . . . x | 4 | 2 2 | 192 * ♦ 5 0 | 10 0 | 10 0 | 5 0 . . . . . o4/3x | 4 | 0 4 | * 480 ♦ 1 4 | 4 6 | 6 4 | 4 1 ----------------+-----+--------+---------+---------+---------+-------+----- x . . . . o4/3x ♦ 8 | 4 8 | 4 2 | 240 * ♦ 4 0 | 6 0 | 4 0 . . . . o3o4/3x ♦ 8 | 0 12 | 0 6 | * 320 ♦ 1 3 | 3 3 | 3 1 ----------------+-----+--------+---------+---------+---------+-------+----- x . . . o3o4/3x ♦ 16 | 8 24 | 12 12 | 6 2 | 160 * | 3 0 | 3 0 . . . o3o3o4/3x ♦ 16 | 0 32 | 0 24 | 0 8 | * 120 | 1 2 | 2 1 ----------------+-----+--------+---------+---------+---------+-------+----- x . . o3o3o4/3x ♦ 32 | 16 64 | 32 48 | 24 16 | 8 2 | 60 * | 2 0 . . o3o3o3o4/3x ♦ 32 | 0 80 | 0 80 | 0 40 | 0 10 | * 24 | 1 1 ----------------+-----+--------+---------+---------+---------+-------+----- x . o3o3o3o4/3x ♦ 64 | 32 160 | 80 160 | 80 80 | 40 20 | 10 2 | 12 * . o3o3o3o3o4/3x ♦ 64 | 0 192 | 0 240 | 0 160 | 0 60 | 0 12 | * 2
o4x o3o3o3o4x . . . . . . . | 128 ♦ 2 5 | 1 10 10 | 5 20 10 | 10 20 5 | 10 10 1 | 5 2 --------------+-----+---------+------------+------------+-----------+---------+----- . x . . . . . | 2 | 128 * ♦ 1 5 0 | 5 10 0 | 10 10 0 | 10 5 0 | 5 1 . . . . . . x | 2 | * 320 ♦ 0 2 4 | 1 8 6 | 4 12 4 | 6 8 1 | 4 2 --------------+-----+---------+------------+------------+-----------+---------+----- o4x . . . . . | 4 | 4 0 | 32 * * ♦ 5 0 0 | 10 0 0 | 10 0 0 | 5 0 . x . . . . x | 4 | 2 2 | * 320 * ♦ 1 4 0 | 4 6 0 | 6 4 0 | 4 1 . . . . . o4x | 4 | 0 4 | * * 320 ♦ 0 2 3 | 1 6 3 | 3 6 1 | 3 2 --------------+-----+---------+------------+------------+-----------+---------+----- o4x . . . . x ♦ 8 | 8 4 | 2 4 0 | 80 * * ♦ 4 0 0 | 6 0 0 | 4 0 . x . . . o4x ♦ 8 | 4 8 | 0 4 2 | * 320 * ♦ 1 3 0 | 3 3 0 | 3 1 . . . . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * 160 ♦ 0 2 2 | 1 4 1 | 2 2 --------------+-----+---------+------------+------------+-----------+---------+----- o4x . . . o4x ♦ 16 | 16 16 | 4 16 4 | 4 4 0 | 80 * * | 3 0 0 | 3 0 . x . . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 6 2 | * 160 * | 1 2 0 | 2 1 . . . o3o3o4x ♦ 16 | 0 32 | 0 0 24 | 0 0 8 | * * 40 | 0 2 1 | 1 2 --------------+-----+---------+------------+------------+-----------+---------+----- o4x . . o3o4x ♦ 32 | 32 48 | 8 48 24 | 12 24 4 | 6 4 0 | 40 * * | 2 0 . x . o3o3o4x ♦ 32 | 16 64 | 0 32 48 | 0 24 16 | 0 8 2 | * 40 * | 1 1 . . o3o3o3o4x ♦ 32 | 0 80 | 0 0 80 | 0 0 40 | 0 0 10 | * * 4 | 0 2 --------------+-----+---------+------------+------------+-----------+---------+----- o4x . o3o3o4x ♦ 64 | 64 128 | 16 128 96 | 36 96 32 | 24 32 4 | 8 4 0 | 10 * . x o3o3o3o4x ♦ 64 | 32 160 | 0 80 160 | 0 80 80 | 0 40 20 | 0 10 2 | * 4
o3o4x o3o3o4x . . . . . . . | 128 ♦ 3 4 | 3 12 6 | 1 12 18 4 | 4 18 12 1 | 6 12 3 | 4 3 --------------+-----+---------+------------+---------------+-------------+----------+---- . . x . . . . | 2 | 192 * ♦ 2 4 0 | 1 8 6 0 | 4 12 4 0 | 6 8 1 | 4 2 . . . . . . x | 2 | * 256 ♦ 0 3 3 | 0 3 9 3 | 1 9 9 1 | 3 9 3 | 3 3 --------------+-----+---------+------------+---------------+-------------+----------+---- . o4x . . . . | 4 | 4 0 | 96 * * ♦ 1 4 0 0 | 4 6 0 0 | 6 4 0 | 4 1 . . x . . . x | 4 | 2 2 | * 384 * ♦ 0 2 3 0 | 1 6 3 0 | 3 6 1 | 3 2 . . . . . o4x | 4 | 0 4 | * * 192 ♦ 0 0 3 2 | 0 3 6 1 | 1 6 3 | 2 3 --------------+-----+---------+------------+---------------+-------------+----------+---- o3o4x . . . . ♦ 8 | 12 0 | 6 0 0 | 16 * * * ♦ 4 0 0 0 | 6 0 0 | 4 0 . o4x . . . x ♦ 8 | 8 4 | 2 4 0 | * 192 * * ♦ 1 3 0 0 | 3 3 0 | 3 1 . . x . . o4x ♦ 8 | 4 8 | 0 4 2 | * * 288 * ♦ 0 2 2 0 | 1 4 1 | 2 2 . . . . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * * 64 ♦ 0 0 3 1 | 0 3 3 | 1 3 --------------+-----+---------+------------+---------------+-------------+----------+---- o3o4x . . . x ♦ 16 | 24 8 | 12 12 0 | 2 6 0 0 | 32 * * * | 3 0 0 | 3 0 . o4x . . o4x ♦ 16 | 16 16 | 4 16 4 | 0 4 4 0 | * 144 * * | 1 2 0 | 2 1 . . x . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 0 6 2 | * * 96 * | 0 2 1 | 1 2 . . . o3o3o4x ♦ 16 | 0 32 | 0 0 24 | 0 0 0 8 | * * * 8 | 0 0 3 | 0 3 --------------+-----+---------+------------+---------------+-------------+----------+---- o3o4x . . o4x ♦ 32 | 48 32 | 24 48 8 | 4 24 12 0 | 4 6 0 0 | 24 * * | 2 0 . o4x . o3o4x ♦ 32 | 32 48 | 8 48 24 | 0 12 24 4 | 0 6 4 0 | * 48 * | 1 1 . . x o3o3o4x ♦ 32 | 16 64 | 0 32 48 | 0 0 24 16 | 0 0 8 2 | * * 12 | 0 2 --------------+-----+---------+------------+---------------+-------------+----------+---- o3o4x . o3o4x ♦ 64 | 96 96 | 48 144 48 | 8 72 72 8 | 12 36 12 0 | 6 6 0 | 8 * . o4x o3o3o4x ♦ 64 | 64 128 | 16 128 96 | 0 36 96 32 | 0 24 32 4 | 0 8 4 | * 6
oo3oo3oo3oo3oo4xx&#x → height = 1
(ax || ax)
o.3o.3o.3o.3o.4o. & | 128 ♦ 6 1 | 15 6 | 20 15 | 15 20 | 6 15 | 1 6
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. .. .. .. .. x. & | 2 | 384 * ♦ 5 1 | 10 5 | 10 10 | 5 10 | 1 5
oo3oo3oo3oo3oo4oo&#x | 2 | * 64 ♦ 0 6 | 0 15 | 0 20 | 0 15 | 0 6
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. .. .. .. o.4x. & | 4 | 4 0 | 480 * ♦ 4 1 | 6 4 | 4 6 | 1 4
.. .. .. .. .. xx&#x | 4 | 2 2 | * 192 ♦ 0 5 | 0 10 | 0 10 | 0 5
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. .. .. o.3o.4x. & ♦ 8 | 12 0 | 6 0 | 320 * ♦ 3 1 | 3 3 | 1 3
.. .. .. .. oo4xx&#x ♦ 8 | 8 4 | 2 4 | * 240 ♦ 0 4 | 0 6 | 0 4
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. .. o.3o.3o.4x. & ♦ 16 | 32 0 | 24 0 | 8 0 | 120 * | 2 1 | 1 2
.. .. .. oo3oo4xx&#x ♦ 16 | 24 8 | 12 12 | 2 6 | * 160 | 0 3 | 0 3
-----------------------+-----+--------+---------+---------+---------+-------+-----
.. o.3o.3o.3o.4x. & ♦ 32 | 80 0 | 80 0 | 40 0 | 10 0 | 24 * | 1 1
.. .. oo3oo3oo4xx&#x ♦ 32 | 64 16 | 48 32 | 16 24 | 2 8 | * 60 | 0 2
-----------------------+-----+--------+---------+---------+---------+-------+-----
o.3o.3o.3o.3o.4x. & ♦ 64 | 192 0 | 240 0 | 160 0 | 60 0 | 12 0 | 2 *
.. oo3oo3oo3oo4xx&#x ♦ 64 | 160 32 | 160 80 | 80 80 | 20 40 | 2 10 | * 12
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