11,000+
Interactive Demonstrations Powered by Notebook Technology »
TOPICS
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Sines of the Dihedral Angles of a Tetrahedron
Let
be a tetrahedron with dihedral angles
,
,
,
,
,
. A theorem relating the sines of the dihedral angles states that
.
Here
,
and
are pairs of opposite edges of the tetrahedron.
Contributed by:
Izidor Hafner
THINGS TO TRY
Rotate and Zoom in 3D
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
DETAILS
A proof is described in [1, pp. 111].
Reference
[1] V. V. Prasolov and I. F. Scharjagin,
Problems in Stereometry
(Russian), Moscow: Nauka, 1989.
RELATED LINKS
Tetrahedron
(
Wolfram
MathWorld
)
Dihedral Angle
(
Wolfram
MathWorld
)
Orthogonal Projection of a Rectangular Solid
(
Wolfram Demonstrations Project
)
A Tetrahedron with Edges of Given Length
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
Sines of the Dihedral Angles of a Tetrahedron
"
http://demonstrations.wolfram.com/SinesOfTheDihedralAnglesOfATetrahedron/
Wolfram Demonstrations Project
Published: February 9, 2017
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Theorem on the Dihedral Angles of an Isosceles Tetrahedron
Izidor Hafner
A Theorem on the Dihedral Angles of a Tetrahedron
Izidor Hafner
Right-Angled Tetrahedron
Izidor Hafner
Monge Point of a Tetrahedron
Izidor Hafner
Altitude of a Tetrahedron Given Its Edges
Izidor Hafner
Inscribed and Circumscribed Spheres of a Tetrahedron
Izidor Hafner
Two Conditions for a Tetrahedron to Be Orthocentric
Izidor Hafner
Spherical Cosine Rule for Angles
Izidor Hafner
Tetrahedron Centers
Ed Pegg Jr
Relations between Plane Angles and Solid Angles in a Trihedron
Izidor Hafner
Related Topics
Polyhedra
Solid Geometry
Triangles
Trigonometric Functions
Browse all topics