Table of Contents
Icosahedron Meaning
The icosahedron is a regular, convex polyhedron with 20 faces. It has 12 vertices and 30 edges. The faces are all triangular and the angles between adjacent faces are all 120 degrees.
What is Platonic Solid?
A Platonic solid is a solid figure that is in the shape of a polyhedron and has faces that are all congruent regular polygons. The Platonic solids are the tetrahedron, the hexahedron or cube, the octahedron, the dodecahedron, and the icosahedron.
Regular Icosahedron
A regular icosahedron is a 20-sided polyhedron that has fivefold symmetry, meaning that it can be divided into five identical parts by any plane that intersects its center. Each of its faces is an equilateral triangle, and its interior is filled with 120 identical equilateral triangles.
Icosahedron Structure
The icosahedron is a 20-sided polyhedron. It has 12 vertices, 20 edges, and 30 faces.
Icosahedron Shape Characteristics
The icosahedron is an important polyhedron because it is the shape of a soccer ball. It has 20 triangular faces, and 30 edges.
Surface Area of Icosahedron
The surface area of an icosahedron is 120 π {\displaystyle 120\pi } square meters.
Volume of Icosahedron
The volume of an icosahedron is (3.14) × (5.72) × (5.72) = 153.62 cubic units.
What is an Icosahedron Shape Used For?
An icosahedron is a polyhedron with 20 faces. It is used in a variety of ways, including in geometry and in crystallography.
Solved Example
A population of 200 plants is to be reduced to 100. Find the number of generations it will take.
We can use the formula:
N= 2N
This will give us:
N= 4
So it will take 4 generations to reduce the population size by half.
1. What is the Volume of the Face Dice Shape Looks Like an Icosahedron With a Side Length of 5 in.
Solution:
Length of the side of the face dice shape looks like an Icosahedron = 5 in
Volume of Icosahedron =
512×(3+5–√)×a3
Volume =
512×(3+5–√)×53
=
62512×(3+5–√)×53
=
62512×(3+5–√)
= 272,71 cm3
Therefore, the volume of the icosahedron is 272,71 cm3.
FAQs
1. What is an icosahedron?
A: An icosahedron is a polyhedron with 20 faces, each of which is an equilateral triangle.
2. How many vertices does an icosahedron have?
A: An icosahedron has 12 vertices.
3. How many edges does an icosahedron have?
A: An icosahedron has 30 edges.
4. What is the dual of an icosahedron?
A: The dual of an icosahedron is a dodecahedron.
5. What is the angle between two adjacent faces of an icosahedron?
A: The angle between two adjacent faces of an icosahedron is 138.19 degrees.
6. What is the surface area of an icosahedron with edge length “a”?
A: The surface area of an icosahedron with edge length “a” is 5√3a².
7. What is the volume of an icosahedron with edge length “a”?
A: The volume of an icosahedron with edge length “a” is (5/12)(3+√5)a³.
8. What is the symmetry group of an icosahedron?
A: The symmetry group of an icosahedron is the group of all rotations and reflections that leave the icosahedron invariant. This group is known as the icosahedral symmetry group or Icosahedral group and denoted by I or Y.
9. What are some real-life examples of an icosahedron?
A: Examples of icosahedral shapes can be found in viruses, geodesic domes, soccer balls, and fullerene molecules.
10. Who discovered the icosahedron?
A: The icosahedron has been known since ancient times and its discovery is not attributed to any one person.
For more visit Atomic Number and Mass Number, Isotopes and Isobars – Representation
