pentellated hexeract,
pentellated hexacross
wrt. hix
wrt. penp
wrt. squatet
wrt. tracube
wrt. pent
(at margins)
- general polytopal classes:
- Wythoffian polypeta
- analogs:
- maximal expanded hypercube eCn
links
| Acronym | stoxog |
| Name |
small terated hexeractihexacontatetrapeton, pentellated hexeract, pentellated hexacross |
| Circumradius | sqrt[2+1/sqrt(2)] = 1.645329 |
|
Inradius wrt. hix | [1+3 sqrt(2)]/sqrt(12) = 1.513420 |
|
Inradius wrt. penp | [5+sqrt(2)]/sqrt(20) = 1.434262 |
|
Inradius wrt. squatet | [1+2 sqrt(2)]/sqrt(8) = 1.353553 |
|
Inradius wrt. tracube | [3+sqrt(2)]/sqrt(12) = 1.274274 |
|
Inradius wrt. pent | (1+sqrt(2))/2 = 1.207107 |
| Coordinates | ((1+sqrt(2))/2, 1/2, 1/2, 1/2, 1/2, 1/2) & all permutations, all changes of sign |
| Volume | [833+579 sqrt(2)]/45 = 36.707326 |
| Surface | [1080+300 sqrt(2)+601 sqrt(3)+30 sqrt(5)]/15 = 174.153910 |
|
Dihedral angles
(at margins) | |
| Face vector | 384, 1920, 4160, 4800, 2904, 728 |
| Confer |
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External links |
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As abstract polytope stoxog is isomorphic to quitoxog.
Incidence matrix according to Dynkin symbol
x3o3o3o3o4x . . . . . . | 384 | 5 5 | 10 20 10 | 10 30 30 10 | 5 20 30 20 5 | 1 5 10 10 5 1 ------------+-----+---------+---------------+-------------------+---------------------+--------------------- x . . . . . | 2 | 960 * | 4 4 0 | 6 12 6 0 | 4 12 12 4 0 | 1 4 6 4 1 0 . . . . . x | 2 | * 960 | 0 4 4 | 0 6 12 6 | 0 4 12 12 4 | 0 1 4 6 4 1 ------------+-----+---------+---------------+-------------------+---------------------+--------------------- x3o . . . . | 3 | 3 0 | 1280 * * | 3 3 0 0 | 3 6 3 0 0 | 1 3 3 1 0 0 x . . . . x | 4 | 2 2 | * 1920 * | 0 3 3 0 | 0 3 6 3 0 | 0 1 3 3 1 0 . . . . o4x | 4 | 0 4 | * * 960 | 0 0 3 3 | 0 0 3 6 3 | 0 0 1 3 3 1 ------------+-----+---------+---------------+-------------------+---------------------+--------------------- x3o3o . . . ♦ 4 | 6 0 | 4 0 0 | 960 * * * | 2 2 0 0 0 | 1 2 1 0 0 0 x3o . . . x ♦ 6 | 6 3 | 2 3 0 | * 1920 * * | 0 2 2 0 0 | 0 1 2 1 0 0 x . . . o4x ♦ 8 | 4 8 | 0 4 2 | * * 1440 * | 0 0 2 2 0 | 0 0 1 2 1 0 . . . o3o4x ♦ 8 | 0 12 | 0 0 6 | * * * 480 | 0 0 0 2 2 | 0 0 0 1 2 1 ------------+-----+---------+---------------+-------------------+---------------------+--------------------- x3o3o3o . . ♦ 5 | 10 0 | 10 0 0 | 5 0 0 0 | 384 * * * * | 1 1 0 0 0 0 x3o3o . . x ♦ 8 | 12 4 | 8 6 0 | 2 4 0 0 | * 960 * * * | 0 1 1 0 0 0 x3o . . o4x ♦ 12 | 12 12 | 4 12 3 | 0 4 3 0 | * * 960 * * | 0 0 1 1 0 0 x . . o3o4x ♦ 16 | 8 24 | 0 12 12 | 0 0 6 2 | * * * 480 * | 0 0 0 1 1 0 . . o3o3o4x ♦ 16 | 0 32 | 0 0 24 | 0 0 0 8 | * * * * 120 | 0 0 0 0 1 1 ------------+-----+---------+---------------+-------------------+---------------------+--------------------- x3o3o3o3o . ♦ 6 | 15 0 | 20 0 0 | 15 0 0 0 | 6 0 0 0 0 | 64 * * * * * x3o3o3o . x ♦ 10 | 20 5 | 20 10 0 | 10 10 0 0 | 2 5 0 0 0 | * 192 * * * * x3o3o . o4x ♦ 16 | 24 16 | 16 24 4 | 4 16 6 0 | 0 4 4 0 0 | * * 240 * * * x3o . o3o4x ♦ 24 | 24 36 | 8 36 18 | 0 12 18 3 | 0 0 6 3 0 | * * * 160 * * x . o3o3o4x ♦ 32 | 16 64 | 0 32 48 | 0 0 24 16 | 0 0 0 8 2 | * * * * 60 * . o3o3o3o4x ♦ 32 | 0 80 | 0 0 80 | 0 0 0 40 | 0 0 0 0 10 | * * * * * 12 snubbed forms: x3o3o3o3o4s
ox3oo4xx xo3oo4xx&#zx → height = 0 (tegum sum of 2 interchanged cubesircoes) o.3o.4o. o.3o.4o. & | 384 | 3 2 2 3 | 3 6 6 1 2 1 9 12 | 1 6 6 3 6 3 4 9 6 18 6 12 | 2 2 3 6 3 5 8 12 18 9 12 | 1 2 1 1 5 4 6 9 3 ------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------ .. .. x. .. .. .. & | 2 | 576 * * * | 2 2 2 0 0 0 0 2 | 1 4 4 1 2 1 0 1 0 4 2 4 | 2 2 2 4 2 0 2 2 6 4 6 | 1 2 1 0 1 2 2 5 2 .. .. .. x. .. .. & | 2 | * 384 * * | 0 3 0 1 1 0 3 0 | 0 3 0 3 3 0 3 3 3 6 0 0 | 1 0 3 3 0 4 6 6 6 3 0 | 1 1 0 1 4 3 3 3 0 .. .. .. .. .. x. & | 2 | * * 384 * | 0 0 3 0 1 1 0 3 | 0 0 3 0 3 3 0 3 0 3 3 6 | 0 1 0 3 3 0 1 3 9 3 9 | 0 1 1 0 1 1 3 6 3 oo3oo4oo oo3oo4oo&#x | 2 | * * * 576 | 0 0 0 0 0 0 4 4 | 0 0 0 0 0 0 2 4 4 8 2 4 | 0 0 0 0 0 4 4 8 8 4 4 | 0 0 0 1 4 2 4 4 1 ------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------ .. o.4x. .. .. .. & | 4 | 4 0 0 0 | 288 * * * * * * * | 1 2 2 0 0 0 0 0 0 0 1 0 | 2 2 1 2 1 0 0 0 0 2 2 | 1 2 1 0 0 1 0 2 1 .. .. x. x. .. .. & | 4 | 2 2 0 0 | * 576 * * * * * * | 0 2 0 1 1 0 0 0 0 2 0 0 | 1 0 2 2 0 0 2 1 2 2 0 | 1 1 0 0 1 2 1 2 0 .. .. x. .. .. x. & | 4 | 2 0 2 0 | * * 576 * * * * * | 0 0 2 0 1 1 0 0 0 0 0 2 | 0 1 0 2 2 0 0 0 3 0 4 | 0 1 1 0 0 0 1 3 2 .. .. .. x.3o. .. & | 3 | 0 3 0 0 | * * * 128 * * * * | 0 0 0 3 0 0 3 0 0 0 0 0 | 0 0 3 0 0 3 6 0 0 0 0 | 1 0 0 1 3 3 0 0 0 .. .. .. x. .. x. & | 4 | 0 2 2 0 | * * * * 192 * * * | 0 0 0 0 3 0 0 3 0 0 0 0 | 0 0 0 3 0 0 0 3 6 0 0 | 0 1 0 0 1 0 3 3 0 .. .. .. .. o.4x. & | 4 | 0 0 4 0 | * * * * * 96 * * | 0 0 0 0 0 3 0 0 0 0 3 0 | 0 0 0 0 3 0 0 0 0 3 6 | 0 0 1 0 0 1 0 3 3 ox .. .. .. .. ..&#x & | 3 | 0 1 0 2 | * * * * * * 1152 * | 0 0 0 0 0 0 1 1 2 2 0 0 | 0 0 0 0 0 3 2 4 2 1 0 | 0 0 0 1 3 1 2 1 0 .. .. xx .. .. ..&#x & | 4 | 1 0 1 2 | * * * * * * * 1152 | 0 0 0 0 0 0 0 1 0 2 1 2 | 0 0 0 0 0 0 1 2 4 2 3 | 0 0 0 0 1 1 2 3 1 ------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------ o.3o.4x. .. .. .. & ♦ 8 | 12 0 0 0 | 6 0 0 0 0 0 0 0 | 48 * * * * * * * * * * * | 2 2 0 0 0 0 0 0 0 0 0 | 1 2 1 0 0 0 0 0 0 .. o.4x. x. .. .. & ♦ 8 | 8 4 0 0 | 2 4 0 0 0 0 0 0 | * 288 * * * * * * * * * * | 1 0 1 1 0 0 0 0 0 1 0 | 1 1 0 0 0 1 0 1 0 .. o.4x. .. .. x. & ♦ 8 | 8 0 4 0 | 2 0 4 0 0 0 0 0 | * * 288 * * * * * * * * * | 0 1 0 1 1 0 0 0 0 0 1 | 0 1 1 0 0 0 0 1 1 .. .. x. x.3o. .. & ♦ 6 | 3 6 0 0 | 0 3 0 2 0 0 0 0 | * * * 192 * * * * * * * * | 0 0 2 0 0 0 2 0 0 0 0 | 1 0 0 0 1 2 0 0 0 .. .. x. x. .. x. & ♦ 8 | 4 4 4 0 | 0 2 2 0 2 0 0 0 | * * * * 288 * * * * * * * | 0 0 0 2 0 0 0 0 2 0 0 | 0 1 0 0 0 0 1 2 0 .. .. x. .. o.4x. & ♦ 8 | 4 0 8 0 | 0 0 4 0 0 2 0 0 | * * * * * 144 * * * * * * | 0 0 0 0 2 0 0 0 0 0 2 | 0 0 1 0 0 0 0 1 2 ox3oo .. .. .. ..&#x & ♦ 4 | 0 3 0 3 | 0 0 0 1 0 0 3 0 | * * * * * * 384 * * * * * | 0 0 0 0 0 2 2 0 0 0 0 | 0 0 0 1 2 1 0 0 0 ox .. xx .. .. ..&#x & ♦ 6 | 1 2 2 4 | 0 0 0 0 1 0 2 2 | * * * * * * * 576 * * * * | 0 0 0 0 0 0 0 2 2 0 0 | 0 0 0 0 1 0 2 1 0 ox .. .. xo .. ..&#x ♦ 4 | 0 2 0 4 | 0 0 0 0 0 0 4 0 | * * * * * * * * 576 * * * | 0 0 0 0 0 2 0 2 0 0 0 | 0 0 0 1 2 0 1 0 0 ox .. .. .. .. xx&#x & ♦ 6 | 2 2 1 4 | 0 1 0 0 0 0 2 2 | * * * * * * * * * 1152 * * | 0 0 0 0 0 0 1 1 1 1 0 | 0 0 0 0 1 1 1 1 0 .. oo4xx .. .. ..&#x & ♦ 8 | 4 0 4 4 | 1 0 0 0 0 1 0 4 | * * * * * * * * * * 288 * | 0 0 0 0 0 0 0 0 0 2 2 | 0 0 0 0 0 1 0 2 1 .. .. xx .. .. xx&#x ♦ 8 | 4 0 4 4 | 0 0 2 0 0 0 0 4 | * * * * * * * * * * * 576 | 0 0 0 0 0 0 0 0 2 0 2 | 0 0 0 0 0 0 1 2 1 ------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------ o.3o.4x. x. .. .. & ♦ 16 | 24 8 0 0 | 12 12 0 0 0 0 0 0 | 2 6 0 0 0 0 0 0 0 0 0 0 | 48 * * * * * * * * * * | 1 1 0 0 0 0 0 0 0 o.3o.4x. .. .. x. & ♦ 16 | 24 0 8 0 | 12 0 12 0 0 0 0 0 | 2 0 6 0 0 0 0 0 0 0 0 0 | * 48 * * * * * * * * * | 0 1 1 0 0 0 0 0 0 .. o.4x. x.3o. .. & ♦ 12 | 12 12 0 0 | 3 12 0 4 0 0 0 0 | 0 3 0 4 0 0 0 0 0 0 0 0 | * * 96 * * * * * * * * | 1 0 0 0 0 1 0 0 0 .. o.4x. x. .. x. & ♦ 16 | 16 8 8 0 | 4 8 8 0 4 0 0 0 | 0 2 2 0 4 0 0 0 0 0 0 0 | * * * 144 * * * * * * * | 0 1 0 0 0 0 0 1 0 .. o.4x. .. o.4x. & ♦ 16 | 16 0 16 0 | 4 0 16 0 0 4 0 0 | 0 0 4 0 0 4 0 0 0 0 0 0 | * * * * 72 * * * * * * | 0 0 1 0 0 0 0 0 1 ox3oo .. xo .. ..&#x & ♦ 5 | 0 4 0 6 | 0 0 0 1 0 0 9 0 | 0 0 0 0 0 0 2 0 3 0 0 0 | * * * * * 384 * * * * * | 0 0 0 1 1 0 0 0 0 ox3oo .. .. .. xx&#x & ♦ 8 | 3 6 1 6 | 0 3 0 2 0 0 6 3 | 0 0 0 1 0 0 2 0 0 3 0 0 | * * * * * * 384 * * * * | 0 0 0 0 1 1 0 0 0 ox .. xx xo .. ..&#x & ♦ 8 | 2 4 2 8 | 0 1 0 0 1 0 8 4 | 0 0 0 0 0 0 0 2 2 2 0 0 | * * * * * * * 576 * * * | 0 0 0 0 1 0 1 0 0 ox .. xx .. .. xx&#x & ♦ 12 | 6 4 6 8 | 0 2 3 0 2 0 4 8 | 0 0 0 0 1 0 0 2 0 2 0 2 | * * * * * * * * 576 * * | 0 0 0 0 0 0 1 1 0 .. oo4xx xo .. ..&#x & ♦ 12 | 8 4 4 8 | 2 4 0 0 0 1 4 8 | 0 1 0 0 0 0 0 0 0 4 2 0 | * * * * * * * * * 288 * | 0 0 0 0 0 1 0 1 0 .. oo4xx .. .. xx&#x & ♦ 16 | 12 0 12 8 | 2 0 8 0 0 2 0 12 | 0 0 1 0 0 1 0 0 0 0 2 4 | * * * * * * * * * * 288 | 0 0 0 0 0 0 0 1 1 ------------------------+-----+-----------------+----------------------------------+-------------------------------------------------+-----------------------------------------+------------------------------ o.3o.4x. x.3o. .. & ♦ 24 | 36 24 0 0 | 18 36 0 8 0 0 0 0 | 3 18 0 12 0 0 0 0 0 0 0 0 | 3 0 6 0 0 0 0 0 0 0 0 | 16 * * * * * * * * o.3o.4x. x. .. x. & ♦ 32 | 48 16 16 0 | 24 24 24 0 8 0 0 0 | 4 12 12 0 12 0 0 0 0 0 0 0 | 2 2 0 6 0 0 0 0 0 0 0 | * 24 * * * * * * * o.3o.4x. .. o.4x. & ♦ 32 | 48 0 32 0 | 24 0 48 0 0 8 0 0 | 4 0 24 0 0 12 0 0 0 0 0 0 | 0 4 0 0 6 0 0 0 0 0 0 | * * 12 * * * * * * ox3oo .. xo3oo ..&#x ♦ 6 | 0 6 0 9 | 0 0 0 2 0 0 18 0 | 0 0 0 0 0 0 6 0 9 0 0 0 | 0 0 0 0 0 6 0 0 0 0 0 | * * * 64 * * * * * ox3oo .. xo .. xx&#x & ♦ 10 | 3 8 2 12 | 0 3 0 2 1 0 18 6 | 0 0 0 1 0 0 4 3 6 6 0 0 | 0 0 0 0 0 2 2 3 0 0 0 | * * * * 192 * * * * ox3oo .. .. oo4xx&#x & ♦ 16 | 12 12 4 12 | 3 12 0 4 0 1 12 12 | 0 3 0 4 0 0 4 0 0 12 3 0 | 0 0 1 0 0 0 4 0 0 3 0 | * * * * * 96 * * * ox .. xx xo .. xx&#x ♦ 16 | 8 8 8 16 | 0 4 4 0 4 0 16 16 | 0 0 0 0 2 0 0 8 4 8 0 4 | 0 0 0 0 0 0 0 4 4 0 0 | * * * * * * 144 * * ox .. xx .. oo4xx&#x & ♦ 24 | 20 8 16 16 | 4 8 12 0 4 2 8 24 | 0 2 2 0 4 1 0 4 0 8 4 8 | 0 0 0 1 0 0 0 0 4 2 2 | * * * * * * * 144 * .. oo4xx .. oo4xx&#x ♦ 32 | 32 0 32 16 | 8 0 32 0 0 8 0 32 | 0 0 8 0 0 8 0 0 0 0 8 16 | 0 0 0 0 2 0 0 0 0 0 8 | * * * * * * * * 36
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