The sphere is actually the best way to cool a drink without diluting it. It was spear-headed by japanese bartending (they know their craft) and it is so effective that Macallan (they make good Scotch) has a ice-ball machine that create spheres of ice that fill the tumbler, and you pour the scotch around it. Edges melt faster. An easy way to convince yourself is to say that the ice cube generally melts into a rounded shape, like an ellipse, if it was a perfect cube it would likely melt into a sphere. If you start as a sphere then it won't be melting into a different shape, instead it will melt evenly and less ice will be lost over the same amount of time. This isn't a great argument, but it is well known that edge effects are important to thermodynamic problems such as this, and it is also well known than high surface areas will transfer heat much more quickly. So, minimizing surface area will get you a sphere.

The sphere is actually the best way to cool a drink without diluting it. It was spear-headed by japanese bartending (they know their craft) and it is so effective that Macallan (they make good Scotch) has a ice-ball machine that create spheres of ice that fill the tumbler, and you pour the scotch around it. Edges melt faster. An easy way to convince yourself is to say that the ice cube generally melts into a rounded shape, like an ellipse, if it was a perfect cube it would likely melt into a sphere. If you start as a sphere then it won't be melting into a different shape, instead it will melt evenly and less ice will be lost over the same amount of time. This isn't a great argument, but it is well known that edge effects are important to thermodynamic problems such as this, and it is also well known than high surface areas will transfer heat much more quickly. So, minimizing surface area will get you a sphere.

Edit: Here is an example of the opposite case.