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Roundest tessellating Polyhedron


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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?

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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)... Fire!" Curtis

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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)... Fire!" Curtis

 

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

 

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

 

Could. Not. Resist.

 

DGv3.0

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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.

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  • 2 weeks later...
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?

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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.

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  • 2 weeks later...

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