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The perspectrix X of a pair of paralogic triangles DeltaA_1A_2A_3 and DeltaB_1B_2B_3 bisects the line joining the two orthocenters H_A and H_B (Johnson 1929, p. 259).

The figure determined by four lines, no three of which are concurrent, and their six points of intersection (Johnson 1929, pp. 61-62). Note that this figure is different from ...

A pentagonal rotunda adjoined to a decagonal prism which is Johnson solid J_(21).

The following table gives the centers of the first Yff circles triangle in terms of the centers of the reference triangle for Kimberling centers X_n with n<=100. X_n center ...

The meeting point of lines that connect corresponding points from homothetic figures. In the above figure, O is the homothetic center of the homothetic figures ABCDE and ...

Two lines PQ and RS are said to be antiparallel with respect to the sides of an angle A if they make the same angle in the opposite senses with the bisector of that angle. If ...

The triangular (or trigonal) dipyramid is one of the convex deltahedra, and Johnson solid J_(12). It is also an isohedron. It is implemented in the Wolfram Language as ...

The tridiminished icosahedron is Johnson solid J_(63). Interestingly, its skeleton has the same degree sequence as the triangular cupola.

The center of the Taylor circle. It has triangle center function alpha_(389)=cosA-cos(2A)cos(B-C) and is Kimberling center X_(389), which is the center of the Spieker circle ...

The gyroelongated pentagonal bicupola is the Johnson solid J_(46), which consists of two pentagonal cupolas, one twisted with respect to the other, adjoined to a decagonal ...