Short Edge Of Deltoidal Icositetrahedron Calculator

Short Edge Of Deltoidal Icositetrahedron Formula:

\[ le(Short) = \frac{4 + \sqrt{2}}{7} \times le(Long) \]

Short Edge Of Deltoidal Icositetrahedron:

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 of a Deltoidal Icositetrahedron. It is a key geometric measurement in this specific polyhedron structure.

2. How Does The Calculator Work?

The calculator uses the mathematical formula:

\[ le(Short) = \frac{4 + \sqrt{2}}{7} \times le(Long) \]

Where:

\( le(Short) \) — Short Edge Of Deltoidal Icositetrahedron (m)
\( le(Long) \) — Long Edge Of Deltoidal Icositetrahedron (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: This formula establishes a precise mathematical relationship between the short and long edges of the deltoidal faces in an icositetrahedron.

3. Importance Of Short Edge Calculation

Details: Calculating the short edge is essential for geometric analysis, 3D modeling, architectural design, and understanding the proportional relationships within deltoidal icositetrahedron structures.

4. Using The Calculator

Tips: Enter the Long Edge Of Deltoidal Icositetrahedron in meters. The value must be positive and greater than zero. The calculator will automatically compute the corresponding short edge length.

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. It is the dual polyhedron of the rhombicuboctahedron.

Q2: Why is the formula specifically (4+√2)/7?
A: This ratio is derived from the geometric properties and trigonometric relationships within the deltoidal icositetrahedron structure, representing the fixed proportion between short and long edges.

Q3: Can this calculator be used for other polyhedrons?
A: No, this specific formula and calculator are designed exclusively for the Deltoidal Icositetrahedron and its unique geometric properties.

Q4: What are practical applications of this calculation?
A: Applications include crystallography, architectural design, mathematical modeling, and creating accurate 3D representations of this specific polyhedron.

Q5: How precise is the calculation?
A: The calculation is mathematically exact based on the geometric properties of the Deltoidal Icositetrahedron, with results rounded to 10 decimal places for practical use.