In this page we will discuss an easy way for solving quickly Octahedron tessellation problem. Similar type of geometric object tessellation can be solved by the method that I'm going to apply here. This type of questions appear frequently in CEED exams.
I took the below example to explain the method in-detail. The question may be asked like that.
By close observation you should find that at each corner there will be four triangles meeting at the junction. So, when we unfold or tessellate the solid octahedron; you should count four or less than four triangle at each corner or edge point as shown in the below pictures for the first option.
Inspect each corner for the number of triangles meeting and ensure that at no corner there will be more than four triangles. If so; that option should probably be the wrong tessellation.
See the corner - check for third option in the below picture. You will find that at corner A the concept matches, but at corner B you will see five triangles meeting. Hence the wrong unfolded view or tessellation is third option.
Try this for second and fourth options and you may find that only four or less than four triangles are meeting at each corner; thus proving as possible tessellations.
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