Table of Contents

## How do I find the volume of a dodecahedron?

Volume of a Dodecahedron

- First, find the square root of 5, which is 2.236.
- Multiply that by 7, which gives you 15.652.
- Add 15 to get 30.652.
- Divide the above sum by 4, which gives you 7.663.
- Now, multiply the above answer by e cubed. (Remember that e is 6, so e cubed is 216.) So, 7.663 x 216 = 1655.208.

**What is a 12 sided 3d shape called?**

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka “twelve” + ἕδρα hédra “base”, “seat” or “face”) or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid.

**What is a 20 sided 3d shape called?**

The icosahedron – 20-sided polyhedron – is frequent. Most often each face of the die is inscribed with a number in Greek and/or Latin up to the number of faces on the polyhedron.

### Can dodecahedron fill space?

The rhombic dodecahedron can be used to tessellate three-dimensional space: it can be stacked to fill a space, much like hexagons fill a plane. This polyhedron in a space-filling tessellation can be seen as the Voronoi tessellation of the face-centered cubic lattice.

**How do u find the area of a decagon?**

The formula to determine the value of the area of a decagon is 5a2/2 × √5+2√5 5 + 2 5 , where ‘a’ is the side length of the decagon.

**What is the volume of a icosahedron?**

Another way to calculate the volume is divide the icosahedron into 3 parts. The height of the pyramid is calculated by the Pythagoras theorem. h² = r² + a². The bottom part of the icosahedron is the same.

#### What is a 100 sided 3d shape called?

Zocchihedron is the label of a 100-sided die, a 3d shape. If a 3d shape with 100 faces is called hecatohedron. In case of two dimensional shapes, a shape with 100 sides is called Hectogon. The relationship between the number of faces, edges and vertices of a 3d shape is given by: F + V = E + 2.

**Do octahedrons pack?**

Its volume can be calculated knowing the volume of an octahedron. It is a space-filling polyhedron. These polyhedra pack together to fill space, forming a 3 dimensional space tessellation or tilling.

**Do tetrahedra fill space?**

A space-filling polyhedron, sometimes called a plesiohedron (Grünbaum and Shephard 1980), is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that the tetrahedron fills space, it in fact does not.

## What is the formula for area of a dodecagon?

The formula for finding the area of a regular dodecagon is: A = 3 × ( 2 + √3 ) × s2 , where A = the area of the dodecagon, s = the length of its side. For example, if the side of a regular dodecagon measures 8 units, the area of this dodecagon will be: A = 3 × ( 2 + √3 ) × s2 .

**How do you calculate the volume of a donut?**

The volume of a torus is calculated by multiplying the area of the cross-section by the circumference of the ring. Volume = π × r2 × 2 × π × R.