# Icosahedron Meaning and Explanation

Regular twenty aspect is a regular polyhedron composed of 20
equilateral triangles, with a total of 12 vertices, 30 edges, and 20 faces.

It
is one of the five Platonic polyhedrons.

Name: Regular twenty
aspect

Scope of application:
Mathematical Sciences

Edge: 30

Surface: 20

**Table of Content**

- Definition
- Nature
- Volume formula
- Calculation formula

## Definition of Icosahedron

Each face of a regular polyhedron is a congruent regular
polygon, and each polyhedral angle is a congruent polyhedral angle.

The
tetrahedron is the least, and the icosahedron is the most.

Regular twenty aspect is a regular polyhedron composed of 20
equilateral triangles, with a total of 12 vertices, 30 edges, and 20 faces.

## What is the Nature of Icosahedron?

1. The circumscribed sphere, inscribed sphere and inscribed
sphere of the icosahedron all exist, and the centers of the three spheres
coincide.

2. The point where the outer, inner, and inner prisms of the
icosahedron coincide is called the center of the icosahedron.

3. The straight line passing through the vertex of the
icosahedron and the center of the regular polyhedron must pass through the
other vertex of the icosahedron, and the distance between the two vertices and
the center of the icosahedron is equal.

4. The two points connecting the center of the regular
icosahedron are called opposite vertices, the two edges connecting the two
pairs of opposite vertices are called opposite edges of the regular
icosahedron, and the two faces surrounded by the opposite edges are called
positive Opposite of the icosahedron.

5. The opposite edges and opposite sides of the icosahedron
are parallel.

### Volume formula

(Where a is the edge length)

### Inscribed regular dodecahedron

On a plane, when a regular polygon is connected to a circle,
the more the number of sides, the higher the percentage of the circle area.

In three-dimensional space, this rule cannot be
generalized-when regular dodecahedron and regular icosahedrons.

When receiving a ball,
the former accounted for about 66.4909%, the latter only accounted for
60.5461%. Some viruses, such as the herpesvirus family, have a capsid of
icosahedron.

Regular icosahedron: 20 faces \ 12 vertices \ 30 edges

If the center of the icosahedron is (0,0,0), the radius of
the circumscribed sphere is 1, the coordinates of each vertex are {(± m, 0, ±
n), (0, ± n, ± m), (± n, ± m, 0)}, where

#### Calculation formula

Distance from body center to each vertex (radius of
circumscribed ball) =

Distance from the center of the body to the center of each
face (inscribed sphere radius) =

The distance from the center of the body to the midpoint of
each edge (tangent sphere radius) =

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