Question

A truncated tetrahedron has _______.
A. 12 vertices
B. 8 faces
C. 18 edges
D. 3 hexagonal faces
This question has multiple correct options

Answer 1

Hint: Think about what the word truncated means. What would happen if all the vertices of a tetrahedron are truncated? Visualize the shape of a tetrahedron with truncated vertices and then calculate the number of vertices, edges, and faces.

Complete step by step answer:
A truncated polyhedron is a polyhedron whose vertices have been cut off and replaced to form a face. The number of faces of the polyhedron will increase by the number of vertices it has. In a tetrahedron, we have 4 faces, 4 vertices, and 6 edges. If we truncate this tetrahedron we will get 4 equilateral triangle faces in place of the vertices.

So, the final structure of the truncated tetrahedron will have 4 faces that are equilateral triangles and 4 faces that were originally the faces of the tetrahedron that will be converted into hexagons. So, a truncated tetrahedron will have a total of 8 faces. Thus, option B is true. Since this shape will have 4 hexagonal faces, option D is false.
- Now let us look at the number of edges that the truncated tetrahedron has. We can see and count the number of edges, consider the edges of the triangular faces first since they do not share edges. These edges add up to 12, there are 6 remaining edges of the hexagonal faces. S, the total number of edges is 18. Thus, option C is true.
- Consider the vertices. We can easily count all the vertices that are present by calculating the number of vertices of the triangular faces. This number will be inclusive of all the vertices that are present on the polyhedron. So, the number of vertices is 12. Thus, option A is true.
So, the correct answer is “Option A,B and C”.

Note: A truncated tetrahedron can be a tetrahedron where only one, two, or three vertices have been cut off. In this case, the number of faces, vertices, and edges will change according to how many vertices were cut off. Since, no such information has been mentioned in the question, here, we will assume that all four vertices of the tetrahedron have been cut off.