X-Nico

3 unusual facts about 5-simplex


5-simplex

The regular 5-simplex is one of 19 uniform polytera based on the 3,3,3,3 Coxeter group, all shown here in A5 Coxeter plane orthographic projections.

T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900

Hexany

So - the geometric figure for the eikosany is the 2D face dual of the 5-simplex or birectified 5-simplex.


10-orthoplex

There are two Coxeter groups associated with the 10-orthoplex, one regular, dual of the 10-cube with the C10 or 4,38 symmetry group, and a lower symmetry with two copies of 9-simplex facets, alternating, with the D10 or 37,1,1 symmetry group.

2 21 polytope

Thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes.

5-demicube

Thorold Gosset identified this series in 1900 as containing all regular polytope facets, containing all simplexes and orthoplexes (5-cells and 16-cells in the case of the rectified 5-cell).

6-orthoplex

There are three Coxeter groups associated with the 6-orthoplex, one regular, dual of the hexeract with the C6 or 4,3,3,3,3 Coxeter group, and a half symmetry with two copies of 5-simplex facets, alternating, with the D6 or 33,1,1 Coxeter group.

6-simplex

The regular 6-simplex is one of 35 uniform 6-polytopes based on the 3,3,3,3,3 Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

7-orthoplex

There are two Coxeter groups associated with the 7-orthoplex, one regular, dual of the hepteract with the C7 or 4,3,3,3,3,3 symmetry group, and a half symmetry with two copies of 6-simplex facets, alternating, with the D7 or 34,1,1 symmetry group.

8-orthoplex

There are two Coxeter groups associated with the 8-cube, one regular, dual of the octeract with the C8 or 4,3,3,3,3,3,3 symmetry group, and a half symmetry with two copies of 7-simplex facets, alternating, with the D8 or 35,1,1 symmetry group.A lowest symmetry construction is based on a dual of a 8-orthotope, called a 8-fusil.

9-orthoplex

There are two Coxeter groups associated with the 9-orthoplex, one regular, dual of the enneract with the C9 or 4,37 symmetry group, and a lower symmetry with two copies of 8-simplex facets, alternating, with the D9 or 36,1,1 symmetry group.

Amplituhedron

In the approach, the on-shell scattering process "tree" is described by a positive Grassmannian, a structure in algebraic geometry analogous to a convex polytope, that generalizes the idea of a simplex in projective space.

Cantellated 5-simplexes

The cantellated 5-simplex is one of 19 uniform polytera based on the 3,3,3,3 Coxeter group, all shown here in A5 Coxeter plane orthographic projections.

Cantellated 6-simplexes

The truncated 6-simplex is one of 35 uniform 6-polytopes based on the 3,3,3,3,3 Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

Curtiss Model N

It quickly became apparent that the aircraft was underpowered, so Curtiss replaced the engine with a 150 hp (112 kW) Hispano-Suiza, manufactured in the United States under license by Wright-Martin's Simplex division (later Wright Aeronautical).

David H. Burrell

There he invented a seamless cheese bandage, silos for the preservation of ensilage, the Burrell-Simplex Link Blade "Simplex" Separator, milk pasteurization systems, churns, butter workers, milk testers and coolers, gang presses, and a universally accepted, patented, BLK milking machine.

Empire Star

He has spent his entire life in a "simplex" society on Rhys, a satellite of a Jovian planet orbiting Tau Ceti.

Encephalitis

Diagnosis is often made with detection of antibodies in the cerebrospinal fluid against a specific viral agent (such as herpes simplex virus) or by polymerase chain reaction that amplifies the RNA or DNA of the virus responsible (such as varicella zoster virus).

Frederick Grinnell

In 2001, Grinnell Fire Protection was merged with the Simplex Time Recorder Company to form SimplexGrinnell, which is the largest fire protection company in the world.

Homer E. Capehart

Packard developed the Simplex mechanism for automatic record changing, and sold the device to Wurlitzer.

Hooghly Engineering and Technology College

The training and placement cell arranges vocational training and placement for students at organizations like L&T, VECC, Air India, Doordarshan, BSNL, DRDO, WBPDCL, WBSEDCL, Eastern Railways (India), NTPC, DVC, CLW, Simplex, Bridge & Roof, KMDA, Shapoorji Pallonji Group, Gannon Dunkerley & Company.

Lecythioscopa

The species was originally placed as Canadia simplex by Charles Walcott in a 1931 publication based on a single specimen.

Mercedes Simplex

When Jellinek received his first Simplex on 1 March 1902 at Nice, he rushed to incorporate it into his Mercedes race team, competing in the Nice-La Turbie hillclimbing race.

Pentellated 6-simplexes

The pentellated 6-simplex is one of 35 uniform 6-polytopes based on the 3,3,3,3,3 Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

Peter Helck

Helck developed an early interest in automobiles, and as a boy caught rides with the race car driver who tested Simplex cars.

QuakeSim

Okada-based elastic fault modeling methods (Disloc, which is a forward model, and Simplex for inverting geodetic data).

Rectified 5-simplexes

It is also one of 19 uniform polytera based on the 3,3,3,3 Coxeter group, all shown here in A5 Coxeter plane orthographic projections.

Rectified 6-simplexes

These polytopes are a part of 35 uniform 6-polytopes based on the 3,3,3,3,3 Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

Runcinated 5-simplexes

These polytopes are in a set of 19 uniform polytera based on the 3,3,3,3 Coxeter group, all shown here in A5 Coxeter plane orthographic projections.

Sheffield-Simplex

Brotherhood sold the London site in 1905 and moved to Peterborough, but could not get permission to build a car factory so the Earl suggested a move to Sheffield where he built a new factory in Tinsley.

Simplex

Stephen Boyd and Lieven Vandenberghe, Convex Optimization, (2004) Cambridge University Press, New York, NY, USA.

Andrew S. Tanenbaum, Computer Networks (4th Ed), (2003) Prentice Hall, ISBN 0-13-066102-3 (See 2.5.3).

Stericated 5-simplexes

These polytopes are a part of 19 uniform polytera based on the 3,3,3,3 Coxeter group, all shown here in A5 Coxeter plane orthographic projections.

Truncated 5-simplexes

The truncated 5-simplex is one of 19 uniform polytera based on the 3,3,3,3 Coxeter group, all shown here in A5 Coxeter plane orthographic projections.


see also