Do you mean like if you drew a line from the surface on one side of the planet, through the Earth's core, to the other side of the planet. What is the longest line that could do that?

Yup... Figured it would be interesting if two people stood on opposite sides of the earth and could claim they were as far apart as possible, or if someone visited both "antipoles" and stood at the locations that were furthest apart.

Wooah, both "antipoles", I've never thought of that. What a great idea. In theory yes, we have the data, but I haven't begun to consider the maths to figure that out.

And then you each put a slice of bread on the ground, and have an Earth sandwich.