2_31_polytope 2_31_polytope

-



1 2_31 polytope

1.1 alternate names
1.2 construction
1.3 images
1.4 related polytopes , honeycombs





2_31 polytope


the 231 composed of 126 vertices, 2016 edges, 10080 faces (triangles), 20160 cells (tetrahedra), 16128 4-faces (3-simplexes), 4788 5-faces (756 pentacrosses, , 4032 5-simplexes), 632 6-faces (576 6-simplexes , 56 221). vertex figure 6-demicube. 126 vertices represent root vectors of simple lie group e7.


this polytope vertex figure uniform tessellation of 7-dimensional space, 331.


alternate names

e. l. elte named v126 (for 126 vertices) in 1912 listing of semiregular polytopes.
it called 231 coxeter bifurcating coxeter-dynkin diagram, single ring on end of 2-node sequence.
pentacontihexa-pentacosiheptacontihexa-exon (acronym laq) - 56-576 facetted polyexon (jonathan bowers)

construction

it created wythoff construction upon set of 7 hyperplane mirrors in 7-dimensional space.


the facet information can extracted coxeter-dynkin diagram, .


removing node on short branch leaves 6-simplex. there 576 of these facets. these facets centered on locations of vertices of 321 polytope, .


removing node on end of 3-length branch leaves 221. there 56 of these facets. these facets centered on locations of vertices of 132 polytope, .


the vertex figure determined removing ringed node , ringing neighboring node. makes 6-demicube, 131, .


images

related polytopes , honeycombs







Comments

Post a Comment

Popular posts from this blog

History First_Bulgarian_Empire

-
1 history 1.1 establishment , consolidation 1.2 internal instability , struggle survival 1.3 territorial expansion 1.4 golden age 1.5 decline , fall history establishment , consolidation bulgaria @ turn of 7th century the bulgars of asparukh moved westwards bessarabia, subdued territories north of danube in modern wallachia, , established in danube delta. in 670s crossed danube scythia minor, nominally byzantine province, steppe grasslands , pastures important large herd stocks of bulgars in addition grazing grounds west of dniester river under control. in 680 byzantine emperor constantine iv (r. 668–685), having defeated arabs, led expedition @ head of huge army , fleet drive off bulgars suffered disastrous defeat @ hands of asparukh @ onglos, swampy region in or around danube delta bulgars had set fortified camp. bulgars advanced south, crossed balkan mountains , invaded thrace. in 681, byzantines compelled sign humiliating peace treaty, forcing them acknowledge bulgaria independ...
Read more

Discography Bruce_Driscoll

-
^ cite error: named reference blogspot1 invoked never defined (see page). ^ cite error: named reference apple1 invoked never defined (see page). ^ tamar kaprelian sinner or saint . rockmeeting.com. retrieved 2015-11-21.  ^ sleepy rebels - bah! humbug! (12/2/10) - stubbys house of christmas . stubbyschristmas.com. 2010-12-03. retrieved 2015-11-21.  ^ sleepy rebels still waiting rebellion . heave media. 2011-05-17. retrieved 2015-11-21.  ^ lana mir - lana mír | credits . allmusic. retrieved 2015-11-21.  ^ trouble, brent (2012-11-28). camera2: made . kick kick snare. retrieved 2015-11-21.  ^ blondfire discusses new record, 80s influences , sibling artistry | life+times . lifeandtimes.com. retrieved 2015-11-21.  ^ freedom fry - dark christmas . record stache. 2012-11-17. retrieved 2015-11-21.  ^ bruce driscoll | credits . allmusic. retrieved 2015-11-21.  ^ earthquake - single freedom fry on itunes . itunes.apple.com. 2012-02-14. retrieved 20...
Read more

Mediterranean_Privateer Ottoman_Algeria

-
purchase of christian slaves french friars (religieux de la mercy de france) in algiers in 1662. despite end of formal hostilities spain in 1580, attacks on christian , catholic shipping, slavery captured, became prevalent in algiers, , main industry , source of revenues of regency. in 17th century, algiers became, along other north african ports such tunis, 1 of bases anglo-turkish piracy. there many 8,000 renegades in city in 1634. (renegades former christians, fleeing law, voluntarily moved muslim territory , converted islam.) hayreddin barbarossa credited tearing down peñón of algiers , using stone build inner harbor. a contemporary letter states: infinity of goods, merchandise jewels , treasure taken our english pirates daily christians , carried allarach [ larache, in morocco], algire , tunis great enriching of mores , turks , impoverishing of christians privateer , slavery of christians originating algiers major problem throughout centuries, leading regular punitive expeditions...
Read more