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What's the simplest shape that has no corners? A circle! That means that most buildings would be built using circular rooms and walls - irregular shapes are possible, too, but they make calculations difficult.

The solution here is to make circular buildings with circular rooms. Putting one room on each story is trivial; putting multiple rooms in a story can be difficult if you need to maximize efficiency. To best do this, we need to look at circle packing in a circle. Take a floor with eight rooms. The optimal arrangement, for eight rooms which are all the same size, is the following:

I modified this in Paint to add in hallways, which are partially circular:

You can also add in smaller rooms or irregular rooms to put the remaining space to use.

DoubleDouble pointed out that this is a three-dimensional problem. Therefore, I propose a solution: Consider the floors, ceilings and walls to be all one surface, by smoothly joining them together, like so:

What's the simplest shape that has no corners? A circle! That means that most buildings would be built using circular rooms and walls - irregular shapes are possible, too, but they make calculations difficult.

The solution here is to make circular buildings with circular rooms. Putting one room on each story is trivial; putting multiple rooms in a story can be difficult if you need to maximize efficiency. To best do this, we need to look at circle packing in a circle. Take a floor with eight rooms. The optimal arrangement, for eight rooms which are all the same size, is the following:

I modified this in Paint to add in hallways, which are partially circular:

You can also add in smaller rooms or irregular rooms to put the remaining space to use.

DoubleDouble pointed out that this is a three-dimensional problem. Therefore, I propose a solution: Consider the floors, ceilings and walls to be all one surface, by smoothly joining them together, like so:

What's the simplest shape that has no corners? A circle! That means that most buildings would be built using circular rooms and walls - irregular shapes are possible, too, but they make calculations difficult.

The solution here is to make circular buildings with circular rooms. Putting one room on each story is trivial; putting multiple rooms in a story can be difficult if you need to maximize efficiency. To best do this, we need to look at circle packing in a circle. Take a floor with eight rooms. The optimal arrangement, for eight rooms which are all the same size, is the following:

http://upload.wikimedia.org/wikipedia/commons/3/3f/Disk_pack8.svg

I modified this in Paint to add in hallways, which are partially circular:

You can also add in smaller rooms or irregular rooms to put the remaining space to use.

DoubleDouble pointed out that this is a three-dimensional problem. Therefore, I propose a solution: Consider the floors, ceilings and walls to be all one surface, by smoothly joining them together, like so:

What's the simplest shape that has no corners? A circle! That means that most buildings would be built using circular rooms and walls - irregular shapes are possible, too, but they make calculations difficult.

The solution here is to make circular buildings with circular rooms. Putting one room on each story is trivial; putting multiple rooms in a story can be difficult if you need to maximize efficiency. To best do this, we need to look at circle packing in a circle. Take a floor with eight rooms. The optimal arrangement, for eight rooms which are all the same size, is the following:

I modified this in Paint to add in hallways, which are partially circular:

You can also add in smaller rooms or irregular rooms to put the remaining space to use.

DoubleDouble pointed out that this is a three-dimensional problem. Therefore, I propose a solution: Consider the floors, ceilings and walls to be all one surface, by smoothly joining them together, like so:

What's the simplest shape that has no corners? A circle! That means that most buildings would be built using circular rooms and walls - irregular shapes are possible, too, but they make calculations difficult.

The solution here is to make circular buildings with circular rooms. Putting one room on each story is trivial; putting multiple rooms in a story can be difficult if you need to maximize efficiency. To best do this, we need to look at circle packing in a circle. Take a floor with eight rooms. The optimal arrangement, for eight rooms which are all the same size, is the following:

http://upload.wikimedia.org/wikipedia/commons/3/3f/Disk_pack8.svg

I modified this in Paint to add in hallways, which are partially circular:

You can also add in smaller rooms or irregular rooms to put the remaining space to use.

What's the simplest shape that has no corners? A circle! That means that most buildings would be built using circular rooms and walls - irregular shapes are possible, too, but they make calculations difficult.

The solution here is to make circular buildings with circular rooms. Putting one room on each story is trivial; putting multiple rooms in a story can be difficult if you need to maximize efficiency. To best do this, we need to look at circle packing in a circle. Take a floor with eight rooms. The optimal arrangement, for eight rooms which are all the same size, is the following:

http://upload.wikimedia.org/wikipedia/commons/3/3f/Disk_pack8.svg

I modified this in Paint to add in hallways, which are partially circular:

You can also add in smaller rooms or irregular rooms to put the remaining space to use.

DoubleDouble pointed out that this is a three-dimensional problem. Therefore, I propose a solution: Consider the floors, ceilings and walls to be all one surface, by smoothly joining them together, like so: