A one million square kilometer hex is ? across

((3/4)^1/2)/2^2/2*6 = 3/4^0.5*3/4 = 3/4^1.5

The distance is one half of (1/(3/4^1.5))^0.5 is ((4/3)^0.75)/2 is 0.62, so a million km hex is 1240 km across and 1075 km high.

No, I'm doing this wrong. A million km square diamond quad is  one thousand across and two thousand high, but cut off the top and bottom halves for three quarters of a million square kilometers, but make that a truncated pair of equilateral triangles 3/4^0.5*1000 km high... is the same calculation. One divided by the square root of three quarters divided by the square root of the square root of three quarters...

Math is my friend, but she's a b! who ghosted me for about five minutes!