Roundest tessellating Polyhedron

[Sociotard]

Of all Hero's good points (and it has many) the one I find I am most likely to incorporate into other game systems is the use of hexagons over squares. Now, of all polygons, the equilateral hexagon is the closest you can come to a circle and still tessellate.

For campaigns that use alot of 3D action (this is why I'm posting in Star Hero), wouldn't it make sense to use a space-filling polyhedron that was round (instead of a hexagonal extrusion)?

If So, what would work best? I know Cubes and Tetrahedrons can, but they aren't especially round. The truncated octahedron can, but it is made of squares AND octagons. The rhombic dodecahedron might work, except for how screwy it looks. So I ask, what is the most spherical polyhedron whose faces are all Identical?

[DigitalGolem]

'tard;

Maybe this would help:

space-filling polyhedrons (http://mathworld.wolfram.com/Tessellation.html)

...although I'm not sure if your criteria can be met. Good luck! Interestingly, according to this page, the tetrahedron actually doesn't fill space, which is a surprise to me. The strange things you learn from gaming....

DGv3.0

[keithcurtis]

It's an interesting theoretical speculation, but unless you have a three-dimensional map where each polyhedron can hold a ship miniaure, it's rather moot. I would simply use hexes and note the elevation. Then use simple hypoteneuse formula for the distance. If angle is important, I suppose you could throw in sime Trig, but I wouldn't play a game like that. I suppose a computer could handle it for you, but I'd rather role-play.

On a related note, I have played using Newtonian mechanics (in Hero) and it's kind of fun. Again, unless you have three or fewer ships, the board becomes a nightmare to do upkeep.

Keith "Mr. Sulu, (X^2 + Y^2 + Z^2)^(1/3)... <i>Fire!</i>" Curtis

[DigitalGolem]

Originally posted by keithcurtis
It's an interesting theoretical speculation, but unless you have a three-dimensional map where each polyhedron can hold a ship miniaure, it's rather moot. I would simply use hexes and note the elevation. Then use simple hypoteneuse formula for the distance. If angle is important, I suppose you could throw in sime Trig, but I wouldn't play a game like that. I suppose a computer could handle it for you, but I'd rather role-play.

On a related note, I have played using Newtonian mechanics (in Hero) and it's kind of fun. Again, unless you have three or fewer ships, the board becomes a nightmare to do upkeep.

Keith "Mr. Sulu, (X^2 + Y^2 + Z^2)^(1/3)... <i>Fire!</i>" Curtis

"Missed! How in the...DOH!!! That's ^(1/2), Captain!"

"Uh, right. Spock? New firing solution!" :D

Could. Not. Resist.

DGv3.0

[keithcurtis]

Originally posted by DigitalGolem
"Missed! How in the...DOH!!! That's ^(1/2), Captain!"

"Uh, right. Spock? New firing solution!" :D

Could. Not. Resist.

DGv3.0

That's probably why they always said something indecipherable like "Deep Space--210 Mark 1"

Keith ":o " Curtis

PS. No Prize to the first person who remembers what classic episode those coordinates were used in. I am such a geek.

[Balok]

Originally posted by keithcurtis
That's probably why they always said something indecipherable like "Deep Space--210 Mark 1"

Keith ":o " Curtis

PS. No Prize to the first person who remembers what classic episode those coordinates were used in. I am such a geek.

Was that where they beamed Nomad so it could explode?

[keithcurtis]

Originally posted by Balok
Was that where they beamed Nomad so it could explode?

Wow! First place to the big-headed puppuet from the First Federation!

Keith " :eek: " Curtis

[McCoy]

Originally posted by keithcurtis
That's probably why they always said something indecipherable like "Deep Space--210 Mark 1"
I believe Lore once explained that this was degrees, horozonal circle mark verticle circle, all relative to the ship, so that 0 mark 0 would be Straight ahead, 180 mark 0 full reverse, 0 mark 90 straight up.

[C_Zeree]

Agggghhh spherical coordinates!!!! :eek:

[Mentor]

Originally posted by keithcurtis
Wow! First place to the big-headed puppuet from the First Federation!

Keith " :eek: " Curtis Hey, did you guys notice that Clint Howard was even bald as a kid? (now that's geeky):D