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Icosahedron

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Q: It has 20 congruent equilateral triangles as faces?
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What shape has 20 congruent equilateral triangles as faces?

An Icosahedron.


If two triangles have three pairs of congruent angles then the triangles are not guaranteed to be congruent?

Correct. Congruency means that two triangles have three pairs of congruent angles and corresponding sides of the same lengths. A pair of triangles with three pairs of congruent angles but sides of different lengths are similar, not congruent.


Is a regular polyhedron a pyramid?

There are five regular polyhedra, also known as the Platonic solids. They are three-dimensional shapes where all of the faces are made up of the same regular polygon.They are:Tetrahedron with four faces (this one is like a pyramid, but with an equilateral triangle for the base and all of the faces)Cube with six faces (all squares)Octahedron with eight faces (all equilateral triangles)Dodecahedron with 12 faces (all regular pentagons)Icosahedron with 20 faces (all equilateral triangles)A square pyramid (like the Egyptian pyramids) is not a regular polyhedron, because it has two different types of regular polygons for faces.


How many short isosceles triangles are needed to build one great Icosahedron?

According to some definitions an icosahedron is considered a Platonic solid so that each of its faces is an equilateral triangle. You would, therefore need three coplanar isosceles triangles to make each face of the icosahedron. Since there are 20 faces in an icosahedron, you would need 60 such triangles.


How many vertices does an icosahedron have?

There is no simple answer to this question.Polyhedra are named according to the number of faces that they have. An icosahedron is a 3-dimensional shape with 20 faces. It could be in the form of a pyramid with a 19-sided polygon as base. In that case, it has 20 vertices. Or it could be in the form of a prism with 18-sided polygons as base and in that case it has 36 vertices. There are several million different configurations, and the number of vertices varies.The regular icosahedron is a Platonic solid with faces that are equilateral triangles. That has 12 vertices.

Related questions

What shape has 20 congruent equilateral triangles as faces?

An Icosahedron.


What 3d shape has 20 congruent equilateral triangles as faces?

An icosahedron.


What has 8 congruent equilateral triangles as faces and 6 vertices?

A solid with 8 faces is an octahedron.As all faces are the same it is a regular octahedron.As such it is one of the five platonic solids - the only five 3D objects that can be regular: the tetrahedron (4 equilateral triangles for the faces), the hexahedron (usually called a cube with 6 square faces), the octahedron (as asked, 8 equilateral triangles for the faces), dodecahedron (12 regular pentagons as faces), icosahedron (20 equilateral triangles as faces).


How many angles does the icosahedron have?

A regular icosahedron has 20 faces (equilateral triangles), 30 edges and 12 vertices.


What is the name of five platonic solids?

1~Tetrahedron *4 faces (made of equilateral triangles) *6 edges *5 vertices 2~Hexahedron (cube) *6 faces (made of squares) *12 edges *8 vertices 3~Octrahedron *8 faces (made up of equilateral triangles) *12 edges *6 vertices 4~Icosahedron *20 faces (made of equilateral triangles) *30 edges *12 verticies 5~Dodecahedron *12 faces (made of pentagons) *30 edges *20 vertices.


How many equilateral faces does a icosahedron have?

It has 20 identical equilateral triangular faces.


What is the shape with each face as an equilateral triangle?

A four sided figure would be a tetrahedron and a 20 sided would be an icosahedron. They both have equilateral triangles for faces so your question is a little incomplete.


Can you name the 3-dimensional shape with 20 congruent triangles as faces?

-17


Can two triangles be similar but not congruent?

Yes. The triangles have the same angle measures but different, similar side lengths. Think of two different sized equilateral triangles. One can have side lengths of 6 inches while the other has side lengths of 20 inches, but they still have congruent angles of 60 degrees. Each ratio of side lengths is equal [6/20=6/20=6/20].


What are platonic solids?

Platonic solids are three-dimensional shapes that have equal sides, angles, and faces. There are five Platonic solids. * The tetrahedron is a four-sided polyhedron with four equilateral triangles for faces. It looks like a three-sided pyramid (where the fourth side is the base). * The cube is a six-sided polyhedron with six squares for faces. * The octahedron is an eight-sided polyhedron with eight equilateral triangles for faces. It looks like two four-sided pyramids attached at their bases. * The dodecahedron is a 12-sided polyhedron with twelve equilateral pentagons for faces. * The icosahedron is a 20-sided polyhedron with twenty equilateral triangles for faces. There are illustrations of them at the websites listed in the links section.


What are the three types of polygons that can be the faces of a Platonic solid?

The polygons are the equilateral triangle, the square, and the regular pentagon. The faces of these platonic solids are made from the following polygons: tetrahedron - 4 triangles cube - 6 squares octahedron - 8 triangles dodecahedron - 12 pentagons icosahedron - 20 triangles


What solid figure has all triangle faces?

There are several: a tetrahedron with 4 equilateral triangles. An 8-sided solid (think of 2 Egyptian pyramids, turn one upside down and put the two square bases together). A 20-sided also has equilateral triangles.

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