What is the sum of the internal angles of a tetrahedron? Solid angle 40

Computational chemistry hexagonal densest stacking known space utilization = 3 root number 2

It is also equal to n*4 3 r 3 v (v = tetrahedral volume = 2 * root number 3 * root number 6 3 * 2 * 1 2 * 1 3 = 2 root number 2 3 ).

So 3 root number 2= n*4 3 r 3 v gives n=1 6 so the four corners of the tetrahedron are enclosed in 1 6 circles, so I think it's 6

Tetrahedron also has internal angles and? Does it make sense to look into this?

The apex angle of the isosceles pie triangle 3, 3,2 is equal to arc cos (3+3-4) 6='

It is a four-way brigade group.

The cosine of the dihedral angle formed by the two adjacent faces of the regular triangular pyramid.

The value is 1 3

Let the edge length be a and the height be 3 2a

cosa=[(3 2a) + 3 2a) -a ] 2* 3 2a* 3 peihuai2a).

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of the top corners. Amount.

arccos

The tetrahedron has six edges, a total of six dihedral angles, and there are too many parameters to directly find the sum of the dihedral angles of any tetrahedron, you can calculate two special tetrahedra first, see if the values are the same, and then decide the next action.

1. Calculate the most special tetrahedron first, let the edge length be 1, its six dihedral angles are equal, and let the size be a, then.

cosa=(1/3)*1*sin60°/1*sin60°=1/3

Therefore, the sum of the dihedral angles of the tetrahedron is 6*arccos(1 3).

2. Calculate a special tetrahedron, the bottom surface is a regular triangle with a side length of 1, and the three side edges are perpendicular to each other, and the length is 1 2 of the bottom side length, (in fact, it is a tetrahedron obtained after the cube only retains three edges with a common vertex).

Obviously, the dihedral angle between the three edges is 2, and the angle between the side and bottom is set to a, cosa=(1 3)*sin60° (1 2)=1 3

Therefore, the sum of the dihedral angles of the tetrahedron is: (3 2)+3*arccos(1 3).

Obviously, the two are not equal, and in conclusion, the value you want is not a fixed value, but a variable related to the length of the six edges of the tetrahedron.

The tetrahedron is four regular triangles, you make the triangle corresponding to the dihedral angle, first set each side of the tetrahedron is 2, then the triangle that is made is the triangle with dihedral angles, the length of each side is respectively, 2, root number 3, root number 3, and then use the knowledge of solving triangles to find the angle, I don't have a calculator, you only ask cos(a) = root number 3 3, find a just that.

The apex angle of the isosceles triangle 3, 3, 2 is equal to arc cos (3+3-4) 6='''

The solid angle is measured by the apex of the cone as the center of the sphere, and the area of the sphere with a radius of 1 is intercepted by the dust touching the cone, and the unit of measurement in the SI system of units is called the sphericity. Similar to the definition of plane angles. On the plane, we define the ratio of an arc differential s to its vector radius r as its corresponding central angle, denoted d = ds r; So the central angle of the whole circumference is 2; Similarly, the ratio of the area element ds on a surface to the square of its vector radius is denoted as d =ds r 2;From this, it can be concluded that the solid angle of the closed sphere is 4.

The solid angle of each vertex of the regular tetrahedron is (3arccos(1 3)- sphericity.

As the midpoint h of AC, connect EH, FH, EH=4, FH=3, and the angle is 90 degrees.

for EHF angles.