# vertex

## Definitions

• WordNet 3.6
• n vertex the point of intersection of lines or the point opposite the base of a figure
• n vertex the highest point (of something) "at the peak of the pyramid"
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Webster's Revised Unabridged Dictionary
• n Vertex (Anat) A turning point; the principal or highest point; top; summit; crown; apex.☞ The principal vertex of a conic section is, in the parabola, the vertex of the axis of the curve: in the ellipse, either extremity of either axis, but usually the left-hand vertex of the transverse axis; in the hyperbola, either vertex, but usually the right-hand vertex of the transverse axis.
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Century Dictionary and Cyclopedia
• n vertex In geometry, the point at which concurrent straights meet.
• n vertex The highest or principal point; apex; top; crown; summit. Specifically— In anatomy and zoology, the crown or top of the head; of man, the dome, vault, or arch of the head or skull, between the forehead and hindhead. See calvarium, sinciput, and cuts under bird, brain, cranium, and skull.
• n vertex In mathematics, a point of a figure most distant from the center; any convex angle of a polygon.
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Chambers's Twentieth Century Dictionary
• n Vertex vėr′teks the top or summit: the point of a cone, pyramid, or angle; (astron.) the zenith:
• n Vertex a vertical line
• n Vertex vėr′teks (anat.) the crown of the head
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## Etymology

Webster's Revised Unabridged Dictionary
L. vertex, -icis, a whirl, top of the head, top, summit, from vertere, to turn. See Verse, and cf. Vortex
Chambers's Twentieth Century Dictionary
L., eddy, summit—vertĕre, to turn.

## Usage

### In literature:

The ordinary head was nearly perfect and of usual volume, but fused with its vertex and reversed was a supernumerary head.
"Anomalies and Curiosities of Medicine" by George M. Gould
Our courses were converging like the sides of an angle, the vertex of which was at the edge of the fog-bank.
"The Sea-Wolf" by Jack London
The Revision, especially with a throne standing on its vertex, has been a work of difficulty, of delicacy.
"The French Revolution" by Thomas Carlyle
It is exceedingly depressed, measuring only about 3.4 inches from the glabello-occipital line to the vertex.
"Lectures and Essays" by T.H. Huxley
Likewise, a considerable thickness of the bone is to be noted, especially of the vertex.
"The Former Philippines thru Foreign Eyes" by Tomás de Comyn
The vertex is orange-coloured, with a black line in the middle.
"Narrative of a Survey of the Intertropical and Western Coasts of Australia] [Volume 2 of 2]" by Phillip Parker King
Head black, orbits of the eyes and a line across the vertex white.
"Discoveries in Australia, Volume 1." by J Lort Stokes
The converging lines commenced in antagonism and increased in bitterness as they neared the vertex.
"History of Kershaw's Brigade" by D. Augustus Dickert
Vertex = supro, pinto.
"English-Esperanto Dictionary" by John Charles O'Connor and Charles Frederic Hayes
Complains constantly of numbness and needle-like pains in vertex.
"Studies in Forensic Psychiatry" by Bernard Glueck
Reddish-yellow: the antennae and vertex, black.
"Journal of the Proceedings of the Linnean Society - Vol. 3" by Various
The peak is the vertex.
"Carpentry for Boys" by J. S. Zerbe
In either case the cranial base, as well as the vertex, will be liable to fracture.
"Surgical Anatomy" by Joseph Maclise
The main branches run towards the vertex, and incisions should, as far as possible, be directed parallel with them.
"Manual of Surgery Volume Second: Extremities--Head--Neck. Sixth Edition." by Alexander Miles
The nostrils open separately or by a single crescentic aperture, near the vertex of the head.
"Encyclopaedia Britannica, 11th Edition, Volume 5, Slice 7" by Various
This distance from the vertex will be the earth's radius.
"A Text-Book of Astronomy" by George C. Comstock
Profound depression with sleeplessness and frequent vertex headache are early symptoms.
"Degeneracy" by Eugene S. Talbot
Thus we have to construct an isosceles triangle, having the angle at the vertex equal to half an angle at the base.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
The cutting plane may pass through the vertex, or it may cut the pyramidal space above the vertex.
"The Teaching of Geometry" by David Eugene Smith
The vertex of the parabola is at the level of the greatest velocity.
"Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 1" by Various
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### In news:

Henry Kromer, 62, Vertex warehouse supervisor.
Vertex Piston & Wrist Pin.
Independent Expert Likes Vertex CF Data.
Vertex Pharmaceuticals (VRTX): Today's Featured Health Care Winner.
Vertex 's 2Q loss narrows on new drug sales.
Vertex Cystic Fibrosis Drug Wins European Approval.
Boston, Vertex 'Top Off' Fan Pier Building.
Vertex Wins Approval for Kalydeco to Treat Cystic Fibrosis.
The 120GB OCZ Vertex 3 solid-state drive offers a lot of speed, but its 240GB bigger brother is still the superior performer.
MMM > News > Vertex gears up sales force for CF drug launch.
OCZ's Vertex 3 is the fastest consumer solid-state drive in the 256GB capacity range.
Vertex Plans to Provide Access to Potential CF Therapy VX-770 for Patients with Critical Medical Need.
MMM > News > Vertex versus Goliaths in HCV drug duel.
Vertex May Make History With Cystic Fibrosis Drug.
Vertex sees positive data from Phase 3 CF study.
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### In science:

Recall that a cutset is a ﬁnite set, C , of vertices not including the root vertex, such that any path from the root vertex to the boundary of the tree intersects the set C at exactly one vertex.
Random walks in random environment on trees and multiplicative chaos
Let the vertices i and j be connected directly to a common vertex k . C is then the probability that vertex i and vertex j are directly connected as well.
Random Geometric Graphs
The clustering coefﬁcient c of a vertex in G is the degree of the vertex divided by the maximal number of edges which could possibly exist between the vertex and all its neighbors.
A Connection-Centric Survey of Recommender Systems Research
Note that in the case where e = {s, t} and t is a terminal vertex of ∆1 , then s is a separating vertex and we may think of ∆ as the union of ∆′ 1 := ∆1 \ e and ∆2 joined at the vertex s .
Automorphisms and abstract commensurators of 2-dimensional Artin groups
Proof Let X denote the complex of groups with underlying complex K , a vertex group hxe i at each vertex Ve , for e ∈ E (∆) , and all other vertex groups trivial.
Automorphisms and abstract commensurators of 2-dimensional Artin groups
GMS], among other important results, Gorbounov, Malikov and Schechtman constructed an N-graded vertex algebra V = `n∈N V(n) from any vertex A-algebroid, such that V(0) = A and the vertex A-algebroid V(1) is isomorphic to the given one.
On certain vertex algebras and their modules associated with vertex algebroids
Then following [GMS], we deﬁne the desired vertex algebra VB associated with a vertex A-algebroid B as a quotient vertex algebra.
On certain vertex algebras and their modules associated with vertex algebroids
For an edge e ∈ E the vertex i(e) is the initial vertex of e, and τ (e) is the terminal vertex of e.
Isomorphism problem for finitely generated fully residually free groups
If there is a vertex v ∈ V such that M = Gv , then deﬁne u = v , otherwise add a vertex u with Gu = M and an edge f with Gf = M so that i(f ) = u and τ (f ) = v (this is a reﬁnement of ∆ at the vertex v).
Isomorphism problem for finitely generated fully residually free groups
Identifying xi pq with the loops in vertex i of QS and y ij pq with the arrows from vertex j to vertex i, the multiplication of two elements of degree 1 in DS , say u = sat and v = s′a′ t′ with a and a′ arrows in QS is then easily seen to be zero unless h(a) = t(a′ ).
Double Poisson structures on finite dimensional semi-simple algebras
VC}| which, for every vertex i ∈ V , equals the fraction of minimal vertex covers containing vertex i ∈ V .
Message passing for vertex covers
In more purely combinatorial terms, they are abstract trees with a distinguished root vertex and a total ordering at each vertex on the set of edges at that vertex pointing away from the root.
Simple omega-categories and chain complexes
If the extension Gn−1 ⊂ Gn is vertex-adding: there is j ∈ [k ], a vertex r of Gn , a vertex s of Gn−1 such that Gn can be obtained from Gn−1 by the addition of the vertex r and of the j -colored edge s → r (or r → s).
Cycles of free words in several independent random permutations with restricted cycle lengths
Now, if no edge with color j has s for beginning vertex (or respectively ending vertex) in Gn−1 /Γ, then by Remark 2.4, Adm(Gn /{t0 = tdi }) is isomorphic to the vertex-adding direct extension of Gn−1/Γ obtained by adding the vertex r and the edge s → r (or respectively r → s).
Cycles of free words in several independent random permutations with restricted cycle lengths
Every vertex of B is either a vertex of Γ or a vertex of some T ∈ T .
On accessibility of finitely generated groups
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