Question

A tetrahedron is shown below made out of paper and 4 tessellations of the same. One of the 4 tessellations is wrong. 
Tick the wrong one. 

Hint:

When checking a net for a tetrahedron, ensure one triangle is surrounded by the other three — this allows the triangles to fold up and meet at the vertices.

Answer 1

Understanding the Tetrahedron Net 
A tetrahedron has: 
4 triangular faces. 
Each triangle must be connected so that all 3 sides of the base triangle are attached to the remaining 3 triangles. 
The net must fold such that all faces meet at the correct angles without overlapping or leaving gaps. 
Correct Tessellations 
Let’s review each option from left to right: 
First Tessellation (Leftmost) — \textcolor{red{Incorrect}} 
This net shows 4 triangles stacked in a straight vertical line. 
Only one triangle (in the center) can act as the base. 
The two triangles above and below cannot all meet at a single point to close the 3D shape. 
Conclusion: This arrangement cannot fold into a tetrahedron. 
Note: This is the incorrect net, and it is correctly marked as such in the solution. 
Second Tessellation — green{Correct}
The triangles are arranged in a fan-like shape, with 3 triangles branching from one base triangle.
Conclusion: This net can fold into a tetrahedron. 
Third Tessellation — green{Correct}
The net forms a “T” shape, with one triangle in the center and the other 3 attached to each edge.
Conclusion: This is a valid configuration for a tetrahedron net. 
Fourth Tessellation — green{Correct}
This configuration also has 3 triangles connected to a central triangle at different sides, allowing correct folding. 
Conclusion: This net is also valid. 
Final Answer 
The first tessellation (the vertical stack of 4 triangles) is the incorrect net and has been correctly ticked as such in the solution image.