This paper aims to present ways in which origami can be used in the mathematics classroom. Origami provides powerful tools for examining mathematical concepts. The authors explain how origami can be used in senior high school and tertiary levels to explore a Platonic octahedron by focusing on connections between mathematical topics. The folding steps to create an octahedron are described and illustrated and then the questions asked at certain folding steps are explained with examples. The questioning during these steps demonstrates how mathematical connections can be established.