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The edge length of a truncated tetrahedron is the measurement of any of the equal-length edges of this polyhedron. A truncated tetrahedron is an Archimedean solid formed by truncating the vertices of a regular tetrahedron.
The calculator uses the formula:
Where:
Explanation: This formula calculates the edge length of a truncated tetrahedron when its volume is known, using the mathematical relationship between volume and edge length for this specific polyhedron.
Details: Calculating the edge length from volume is essential in geometry, architecture, and materials science where truncated tetrahedrons are used. It helps in determining the physical dimensions of objects with this shape.
Tips: Enter the volume of the truncated tetrahedron in cubic meters. The volume must be a positive value greater than zero.
Q1: What is a truncated tetrahedron?
A: A truncated tetrahedron is an Archimedean solid obtained by cutting off the corners of a regular tetrahedron. It has 4 regular hexagonal faces and 4 equilateral triangular faces.
Q2: What are the units for edge length?
A: The edge length is typically measured in meters (m), but can be in any length unit as long as the volume is in the corresponding cubic unit.
Q3: Can this formula be used for any polyhedron?
A: No, this specific formula applies only to truncated tetrahedrons. Other polyhedrons have different volume-to-edge-length relationships.
Q4: What if I have the edge length and want to find the volume?
A: The formula can be rearranged to calculate volume from edge length: \( V = \frac{23 \times \sqrt{2} \times l_e^3}{12} \)
Q5: Are there practical applications of truncated tetrahedrons?
A: Yes, truncated tetrahedrons appear in crystal structures, architectural designs, and molecular models due to their stable geometric properties.