Okay I have tried to make a truncated cube because I thought "Well If I do cycles from a platonic solid to its dual and I already have the cube and the cube was easiest to make maybe the truncated cube is next and it has 8 octagons and 8 triangles. I was already thinking "Everything has to be equilateral since it is from a cube". The angle between each side of the octagon is 135 degrees and I tried the 1 inch that worked for my other 4 solid figures I made and the one I recently made which is the truncated tetrahedron and I thought I could fit 6 1 inch octagons and 8 equilateral triangles of the same length on a sheet of construction paper but I could only fit 1 octagon and a few triangles. I tried halfing the length of each of the sides and it still did not work even though I could fit more. Do I need more paper for it than I thought I would need or do I need to half the length again to 1/4 inch?

If I understand you correctly, You are making a solid from 6 octagons and 6 equilateral triangles, with all sides/edges equal to 1 inch? In that way, each octagon should be less than 2.5 inches wide and 2.5 inches tall.

[To prove: take a 2.5 inch square, measure a fourth of the way (.625 inches) on both sides from each corner/vertex and mark. Draw a line connecting each pair of marks at each corner. Slice off all 4 corners along the line to form 8 new corners of 45 degrees each.The sides/edges should all be a bit more than 1 inch each.]

Make sure you are measuring correctly. The triangles are 1 inch wide at the base and, because they are equilateral (60 degree), less than an inch high. You should be able to close-pack the octagons (2-1-2-1 staggered array)with plenty of room for the triangles, if I'm not mistaken. I'm assuming you aren't adding tabs, but even then, it should fit, unless my geometry has gone horribly, horribly wrong! Disclaimer: I am not a Math major or a mathematician of any kind, but I do like origami and papercrafts! Good Luck!