# parallelopiped

## Definitions

• WordNet 3.6
• n parallelopiped a prism whose bases are parallelograms
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Webster's Revised Unabridged Dictionary
• n Parallelopiped (Geom) A solid, the faces of which are six parallelograms, the opposite pairs being parallel, and equal to each other; a prism whose base is a parallelogram.
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Century Dictionary and Cyclopedia
• n parallelopiped See parallelepiped.
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## Etymology

Webster's Revised Unabridged Dictionary
Gr. para`llhlos parallel + 'epi`pedon a plane surface, 'epi`pedos on the ground, or level with it, level, flat; 'epi` on + pe`don the ground: cf. F. parallélopipède,

## Usage

### In literature:

His first balloon was a small parallelopiped in very thin taffeta, containing less than seventy-eight cubic inches of air.
"Wonderful Balloon Ascents" by Fulgence Marion
The thinner walls are composed of a single depth of the parallelopiped, while the thicker ones consist of two or more depths.
"First Across the Continent" by Noah Brooks
And if so, why not also angles, triangles, parallelograms, parallelopipeds, and bodies?
"Essays and Miscellanies" by Plutarch
On Friday last we abandoned our former works in parallelopipeds and proceeded to truncated prisms.
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### In science:

Observe that any n × n matrix with entries ±1 can have determinant at most nn/2 (since the magnitude of the determinant equals the volume of a n-dimensional parallelopiped, all of whose edges have length √n); this is also known as Hadamard’s inequality.
On the singularity probability of random Bernoulli matrices
The theorem actually holds for parallelopipeds with the same roundness condition, i.e., convex bodies speciﬁed by an n × n real matrix A as {x ∈ Rn : ∀ 1 ≤ i ≤ n |Ai · x| ≤ 1} where Ai denotes the i’th row of A.
Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
When K is a parallelopiped speciﬁed by a matrix A, the oracle outputs YES if kAqk∞ ≤ 1 and NO otherwise.
Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
We will use the distribution D on parallelopipeds (or matrices, equivalently).
Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
Since each double band has two components, the intersection of all the n bands associated to a particular region Ai , namely ∩n j=1Bij , is the union of 2n congruent parallelopipeds.
Dispersion of Mass and the Complexity of Randomized Geometric Algorithms
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