Short Edge of Deltoidal Icositetrahedron given Midsphere Radius Calculator

Formula Used:

\[ l_{Short} = \frac{4+\sqrt{2}}{7} \times \frac{2 \times r_m}{1+\sqrt{2}} \]

Short Edge of Deltoidal Icositetrahedron (l_Short):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Short Edge of Deltoidal Icositetrahedron?

The Short Edge of Deltoidal Icositetrahedron is the length of the shortest edge of the identical deltoidal faces that make up the Deltoidal Icositetrahedron, a Catalan solid with 24 deltoidal (kite-shaped) faces.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l_{Short} = \frac{4+\sqrt{2}}{7} \times \frac{2 \times r_m}{1+\sqrt{2}} \]

Where:

\( l_{Short} \) — Short Edge of Deltoidal Icositetrahedron (m)
\( r_m \) — Midsphere Radius of Deltoidal Icositetrahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula calculates the length of the shortest edge based on the midsphere radius, which is the radius of the sphere tangent to all edges of the polyhedron.

3. Importance of Short Edge Calculation

Details: Calculating the short edge is important for understanding the geometric properties of the Deltoidal Icositetrahedron, including its surface area, volume, and other dimensional relationships in geometric modeling and 3D design applications.

4. Using the Calculator

Tips: Enter the midsphere radius in meters. The value must be positive and greater than zero. The calculator will compute the corresponding short edge length of the Deltoidal Icositetrahedron.

5. Frequently Asked Questions (FAQ)

Q1: What is a Deltoidal Icositetrahedron?
A: A Deltoidal Icositetrahedron is a Catalan solid with 24 deltoidal (kite-shaped) faces, 26 vertices, and 48 edges. It is the dual of the rhombicuboctahedron.

Q2: What is the midsphere radius?
A: The midsphere radius is the radius of the sphere that is tangent to all edges of the polyhedron. It lies midway between the insphere and circumsphere.

Q3: Are there other edges in a Deltoidal Icositetrahedron?
A: Yes, besides the short edge, the Deltoidal Icositetrahedron also has medium and long edges, each with different lengths and geometric relationships.

Q4: What are typical applications of this calculation?
A: This calculation is useful in geometry research, 3D modeling, architectural design, and mathematical education where precise dimensional relationships of polyhedra are required.

Q5: How accurate is this formula?
A: The formula is mathematically exact for a perfect Deltoidal Icositetrahedron. The accuracy of the result depends on the precision of the input value.