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Vsevolod [243]
3 years ago
9

What type of polygon would a slice of a hexahedron at a vertex create? Explain. What type of polygon would a slice of an icosahe

dron at a vertex create? Explain.

Mathematics
1 answer:
harina [27]3 years ago
3 0

Answer:

  • hexahedron: triangle or quadrilateral or pentagon
  • icosahedron: quadrilateral or pentagon

Step-by-step explanation:

<u>Hexahedron</u>

A hexahedron has 6 faces. A <em>regular</em> hexahedron is a cube. 3 square faces meet at each vertex.

If the hexahedron is not regular, depending on how those faces are arranged, a slice near a vertex may intersect 3, 4, or 5 faces. The first attachment shows 3- and 4-edges meeting at a vertex. If those two vertices were merged, then there would be 5 edges meeting at the vertex of the resulting pentagonal pyramid.

A slice near a vertex may create a triangle, quadrilateral, or pentagon.

<u>Icosahedron</u>

An icosahedron has 20 faces. The faces of a <em>regular</em> icosahedron are all equilateral triangles. 5 triangles meet at each vertex.

If the icosahedron is not regular, depending on how the faces are arranged, a slice near the vertex may intersect from 3 to 19 faces.

A slice near a vertex may create a polygon of 3 to 19 sides..

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