17:
416:
399:
Conway, J. H.; Sloane, N. J. A. (1991). "The Cell
Structures of Certain Lattices". In Hilton, P.; Hirzebruch, F.; Remmert, R. (eds.).
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to be nonnegative or nonpositive. Such a subset is defined by a system of inequalities:
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169: > 0 · · · ε
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110: ≥ 0 · · · ε
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67:. By independent selections of half-space signs, there are 2 orthants in
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In two dimensions, there are four orthants (called quadrants)
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is a subset defined by a system of strict inequalities
308:(or hypercube) – a family of regular polytopes in
59:-dimensions can be considered the intersection of
312:-dimensions which can be constructed with one
295:-dimensions which can be constructed with one
326:-dimensions, with one vertex in each orthant.
8:
159: > 0 ε
100: ≥ 0 ε
82:is a subset defined by constraining each
336:
214:In three dimensions, an orthant is an
271:-dimensions and is important in many
7:
436:The facts on file: Geometry handbook
403:. Berlin: Springer. pp. 89–90.
353:(2nd ed.). New York: Springer.
322:– generalization of a rectangle in
263:is the generalization of the first
207:In two dimensions, an orthant is a
200:In one dimension, an orthant is a
14:
1:
438:, Catherine A. Gorini, 2003,
287:(or orthoplex) – a family of
409:10.1007/978-3-642-76709-8_5
481:
55:In general an orthant in
273:constrained optimization
401:Miscellanea Mathematica
350:Advanced Linear Algebra
316:in each orthant space.
302:in each orthant space.
21:
74:More specifically, a
52:in three dimensions.
19:
84:Cartesian coordinate
71:-dimensional space.
63:mutually orthogonal
261:nonnegative orthant
256:, one per orthant.
249:-dimensions with 2
134:is +1 or −1.
48:in the plane or an
36:is the analogue in
460:Euclidean geometry
376:Weisstein, Eric W.
183: > 0,
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418:978-3-642-76711-1
289:regular polytopes
229:defined the term
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306:Measure polytope
243:regular polytope
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430:Further reading
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239:orthant complex
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42:Euclidean space
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285:Cross polytope
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196:By dimension:
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137:Similarly, an
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379:"Hyperoctant"
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345:Roman, Steven
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187:where each ε
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139:open orthant
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128:where each ε
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227:Neil Sloane
223:John Conway
65:half-spaces
34:hyperoctant
454:Categories
331:References
275:problems.
384:MathWorld
320:Orthotope
235:orthoplex
347:(2005).
279:See also
265:quadrant
209:quadrant
46:quadrant
26:geometry
446:, p.113
297:simplex
251:simplex
30:orthant
442:
415:
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314:vertex
300:facets
254:facets
216:octant
50:octant
241:as a
237:from
44:of a
28:, an
440:ISBN
413:ISBN
355:ISBN
259:The
225:and
405:doi
291:in
267:to
245:in
202:ray
141:in
78:in
32:or
24:In
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324:n
310:n
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190:i
180:n
176:x
172:n
167:2
164:x
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154:x
151:1
149:ε
143:R
131:i
121:n
117:x
113:n
108:2
105:x
102:2
98:1
95:x
92:1
90:ε
80:R
69:n
61:n
57:n
38:n
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