trihedral

[trahy-hee-druhl]

adjective

Geometry.

1. having, or formed by, three planes meeting in a point.

   a trihedral angle.

noun

1. a trihedron.

trihedral

/ traɪˈhiːdrəl /

adjective

1. having or formed by three plane faces meeting at a point

noun

1. a figure formed by the intersection of three lines in different planes

Other Word Forms

• subtrihedral adjective

Word History and Origins

Origin of trihedral¹

First recorded in 1780–90; tri- + -hedral

Word History and Origins

Origin of trihedral¹

C18: from _tri- + Greek hedra base, seat + _-al ¹

Example Sentences

Trihedral, trī-hē′dral, adj. having three equal sides.—n.

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In solid geometry it is used only in a proposition relating to the volumes of two triangular pyramids having a common trihedral angle, and this is usually omitted.

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We get, for instance, from I. 4, the 687 theorem, If two trihedral angles have the angles of two faces in the one equal to the angles of two faces in the other, and have likewise the angles included by these faces equal, then the angles in the remaining faces are equal, and the angles between the other faces are equal each to each, viz. those which are opposite equal faces.

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The connexion indicated between triangles and trihedral angles will also be recognized in Prop.

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If three planes pass through a common point, and if they bound each other, a solid angle of three faces, or a trihedral angle, is formed, and similarly by more planes a solid angle of more faces, or a polyhedral angle.

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