Physics of Tall Structures

Yesterday, in Physics class, the activity was to build the tallest structure out of newspaper and some tape. My group members came up with the idea of crumpling up paper to make a "small" base and thought that it would actually support the weight of the entire building.It was one of the most ridiculous designs ever. In the end, as I expected, the center of gravity for the structure was too high and the height needed to be shortened so it doesn't fall over by itself. Our's was the shortest.
The best building design would be to make a triangular/rectangular pyramid at the bottom with rolled up newspaper (as other groups did). After that, roll around 2-3 full pages and tape one on top of the other. The base should be able to sustain the weight of the structure still. Above that, the newspaper needs to be ripped/cut into smaller pieces which would be made into prisms, (triangular or rectangular and simple). A full page of newspaper could create a length of maybe 2 meters, saving materials and making the top very light. The reset of the paper can be user to add supports to the base. This would make the center of gravity very low therefore it wouldn't topple over that easily.