hypercube
a simple capture of acomplex optical sculpture made of mirrors and thin neon lights...
A hypercube of dimension n has 2n "sides" (a 1-dimensional line has 2 end points; a 2-dimensional square has 4 sides or edges; a 3-dimensional cube has 6 2-dimensional faces; a 4-dimensional tesseract has 8 cells). The number of vertices (points) of a hypercube is 2n (a cube has 23 vertices, for instance).
A simple formula to calculate the number of "n-2"-faces in an n-dimensional hypercube is: 2n2 − 2n
The number of m-dimensional hypercubes (just referred to as m-cube from here on) on the boundary of an n-cube is
, where and n! denotes the factorial of n.
For example, the boundary of a 4-cube (n=4) contains 8 cubes
(3-cubes), 24 squares (2-cubes), 32 lines (1-cubes) and 16 vertices
(0-cubes).
This identity can be proved by combinatorial arguments; each of the 2n vertices defines a vertex in a m-dimensional boundrary. There are ways of choosing which lines ("sides") that defines the subspace that the boundrary is in. But, each side is counted 2m times since it has that many vertices, we need to divide with this number. Hence the identity above.
Comments and faves
5y12u3k, *melkor*, thecreativelens, Grant MacDonald, and 28 other people added this photo to their favorites.
mareluna265 (50 months ago | reply)
un'ltro scatto molto particolare... bello! notte..:-)
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Michele Greco (aka djmike_foh) (50 months ago | reply)
che figata! bellissima la geometria in questa foto
salambó (50 months ago | reply)
Wow. It´s amazing.
Marianna Carolina Sale (50 months ago | reply)
molto bella Mario! complimenti!
seveDB (50 months ago | reply)
Anche questa e bela, come sempre.
thecreativelens (50 months ago | reply)
Very nice.
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Grant MacDonald (50 months ago | reply)
very nice. Love the geometry!
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goodoldchuck (50 months ago | reply)
That's really wonderful!
desalinado (50 months ago | reply)
inside the cube :) very clear.
LadyBebo (50 months ago | reply)
uao...la foto è belissima, la scultura doveva essere un vero trip!
Stefania Maria Livraghi (50 months ago | reply)
Molto originale, bella!
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peggy. (50 months ago | reply)
terrific abstract!
I saw this Great Photo in: Photos to Smile About Where QUALITY Counts!!
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albaflickr (50 months ago | reply)
I saw this best of the best picture in
~~ The Best Picture Gallery group ~~
yellowrubberduck (50 months ago | reply)
Colour Art Award
jawadn_99 (50 months ago | reply)
I found this Cool image in
**The Coolest Damn Cool Photographers in the World**
Claudio Poblete (50 months ago | reply)
very good!
I found this Cool image in
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berlondoner (50 months ago | reply)
Fantastic picture, congratulation!
Hi, I'm an admin for a group called Here, There and Everywhere, and we'd love to have this added to the group!
cool_colonia4711 (50 months ago | reply)
I saw this Great Photo in: Photos to Smile About
Fotourbana (50 months ago | reply)
Vivid
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raisinsawdust (50 months ago | reply)
You deserve another cube
Flickr Cubism Award:
The Great Artistic Photographer
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antonychammond (50 months ago | reply)
Great geometric patterns...
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Mr. Wondering (50 months ago | reply)
Quite Oblique!
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roy_mac_an_iarla (50 months ago | reply)
Great shot, of what is obviously a cool sculpture!
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amiplim_ (50 months ago | reply)
I saw this Great Photo in: Photos to Smile About
giuhal (50 months ago | reply)
adoro le geometrie :D ben riuscite
See in not only photos
mannaggia la pupazza
eskipy (TGN) (50 months ago | reply)
Incredible!! this image !
Bluesrose (50 months ago | reply)
..and beautiful! :)
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Len Janes Photography (50 months ago | reply)
Great capture, nice shot.
Congratulations on receiving your Macro Award, and I think this photo deserves another one!
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This photo took my BREATH away
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slipper buddha (50 months ago | reply)
simple made, but beautifull space...
nicolas muguet (50 months ago | reply)
Amazing !
Great shot
Congratulations on receiving your Macro Award, and I think this photo deserves another one!
inge helene (50 months ago | reply)
Geometrical beauty. Fascinating different tones of blue!
I saw this Great Photo in: Photos to Smile About
KagedFish (50 months ago | reply)
Seen in :
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very cool!!!!
DoodleDancer (50 months ago | reply)
what depth!
Saw this out-of-this-world image at So Intergalactic!
kmrphotography (50 months ago | reply)
Vivid
jan4photos (50 months ago | reply)
fantastic geometry, great spatial awareness
Vivid
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sergio bretel (50 months ago | reply)
Abstract Art Award
Niquitin (50 months ago | reply)
Beautiful - like an organism. Wonderful depth!
deepintheforestcat (50 months ago | reply)
Outstanding.
We Invite you to submit your work to the group
This art piece is recognized as a very beautiful work!!!
Outstanding Art!!!!!!!!
atomareaufruestung (50 months ago | reply)
very interesting shot!
Etrusia UK (50 months ago | reply)
Hi, I'm an admin for a group called Picture Perfect>>>>(pst 1/cmnt3)>>>> New Contest Open, and we'd love to have this added to the group!
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mon sobriquet (50 months ago | reply)
Abstract Art Award
~morsus~ (50 months ago | reply)
I saw this spacy photo in : ~PAINTING WITH SPACE~
The Lady of Shalot [mostly offline these days] (50 months ago | reply)
Notevole intreccio, e bello anche il colore.
Mi piacciono i neon... viste le installazioni a Villa Panza (Varese)?
Nature made this excellent work
with your hand support.
Seen in Alchimia Fotografica.
Marcus Surrealleous (50 months ago | reply)
**Elle** (50 months ago | reply)
Ciao Artista :)
Incredibile il tuo occhio... la tua anima... :)
Buonissimo weekend con un bacio
this is an exceptional image
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77dps (50 months ago | reply)
Abstract Art Award
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chonyta (50 months ago | reply)
Mario, this is so ingenious!
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Macro Award
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Definitely a winner!!!
You deserve another one.
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I Think this is Art !
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maybeetle (50 months ago | reply)
veramente spettacolare...
*Katch* (50 months ago | reply)
I saw this great diagonal shot in
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eYe_image (50 months ago | reply)
Abstract Art Award