Tetra Octa Hedron?
Geometry
Level
4
The face of a tetrahedron is glued to the face of an octahedron so that the edges of the triangles match up perfectly. How many sides does the resulting polyhedron have?
Try more questions on Platonic Solids
12
9
10
7
8
5
11
6
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1 solution
The tetrahedron has 4 faces, and the octahedron has 8. So, the total is 12. The two that are glued together go away, so that's 10, and finally, the angles are such that the 3 remaining faces of the tetrahedron line up perfectly with three faces of the octahedron, so the get "merged", thus losing 3 additional faces. So the total number of faces in the resulting polyhedron is 1 2 − 2 − 3 = 7 .