A large imaginary cube:

[Zane_C]

I was curious as to how large a cube would be, if the building materials were one cube per possible 3x3 configuration. This has probably already been posted somewhere, but anyway.
At first the value I obtained seemed too low, but I can't see any errors in the basic calculations. Please point out any mistakes.

Sorry for the bad setting out, I've never really used the "\( ".

Number of cubes multiplied by the volume of one.
\( 43,252,003,274,489,856,000 * 5.7^3
= 8,009,968,242,412,599,902,208 cm^3 \)
Divide by 1 quadrillion to convert to cubic kilometres \( = 8,009,968.242412599902208 km^3 \)

The cubed root of that equals a side length of 200.083 km. \)

 

[Cubenovice]

nevermind

 

[MTGjumper]

Heh, cubed route

 

[Kirjava]

lol puzzle theory

 

[Zane_C]

lol puzzle theory

It was either the off-topic or this, I made my choice.

 

[Godmil]

Okie dokie, this is super rough, but here is your cube in relation to the moon.

Was going to do it against the earth, but I forgot just how massive the Earth is even up close the cube was a spec.

 

[cmhardw]

Yeah, your math looks solid. I got the same result when I tried it.

For another visual representation: From the Megapenny project one quintillion pennies would look like this. So imagine 43 of these cubes plus a about a quarter of another cube. This would be if you are using pennies of course, but it's still mind blowing.

 

[slowhand]

Google calculator give a different answer... namely:

43 252 003 274 489 856 000 * 5.7 (cm^3) = 246 536.419 km^3

I've not stop to evaluate why though.

 

[Forte]

it's (5.7cm)^3 not 5.7 (cm^3) >_>

 

[slowhand]

Cool, I typo'ed the expression.

 

[cuBerBruce]

Or you could create a slightly non-cubic stack 3,538,944 cubes long by 3,499,200 cubes wide by 3,492,720 cubes high.

 

[Rinfiyks]

For 2x2x2 (at 5 cm) it's only ~460 cubic metres. That's a cube of cubes with side length of just ~7.7 metres!
For 4x4x4 the cube of cubes has a side length of 780 AU.

 

[Zane_C]

For 2x2x2 (at 5 cm) it's only ~460 cubic metres. That's a cube of cubes with side length of just ~7.7 metres!
For 4x4x4 the cube of cubes has a side length of 780 AU.

Interesting, above 3x3 it just gets pretty ridiculous to comprehend.

 

[Rinfiyks]

Interesting, above 3x3 it just gets pretty ridiculous to comprehend.

It does. Which got me wondering, how big would it be for megaminxes?
From page 25, dodecahedrons will use ~90.4% of the space because they cannot be packed to leave no gaps. I don't know the side length of a megaminx because I left mine at uni... anyone want to work it out?

 

[ben1996123]

5x5:

Spoiler

282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000 * 6.5³ = 282,870,942,277,741,856,536,180,333,107,150,328,293,127,731,985,672,134,721,536,000,000,000,000,000 * 274.625 = 77683432523024857351248523979551158907500203396565209997901824000000000000000 which is apparently about 0.07% of the atoms in the universe.

77683432523024857351248523979551158907500203396565209997901824000000000000000 / 1 quadrillion = 77683432523024857351248523979551158907500203396565209997901.824 km³

³√77683432523024857351248523979551158907500203396565209997901.824 = ~42,668,705,673,237,827,385.92km side length, just about half a quintillion km less than the amount of 3x3 permutations, about 4.5 million light years per side

Side length of 1.38 megaparsecs

EDIT:

random: I just asked my mum to guess the side length (I was quite bored).

her: erm... massive
me: how massive
her: enormous, like, 9 feet
me: more -.-
her: 32 feet?
me: trillions more
her: oh...