These are four of the platonic solids (cube, octahedron, dodecahedron, and icosahedron). The last four pictures use colour to illustrate the duality of the solids.
These are two variations on the basic vase producing fold; treatment of the corners determines whether the vase looks like a flower or has sharp spiky bits.
This is a ten sided vase made by starting with a ten sided regular polygon and folding carefully. The resulting vase is about 2 cm tall and 5 cm wide from a starting sheet approximatly 15 cm in diameter. (slightly smaller diameter; the square sheet was trimmed to a decagon.)
This flower was built from 6 squares of paper, where the length of each square is 2/3rds of the previous square. At those proportions the boxes nestle nicely inside on another.