QA-Tr-2: (Quadri-)Perspective QA-Triple Triangles


Below are combinations of Triple Triangles that exhibit a (Quadri-)Perspective relationship, along with their corresponding perspector. The Triple Triangles are defined by QG-, QL-, and QA-points, which generate the configurations within the QA or QL environment.

Triple Triangle-1 Triple Triangle-2 Perspector
QG-P1 QG-P2 QA-P10
QG-P1 QG-P4 QA-P1
QG-P1 QG-P8 QA-P1
QG-P1 QG-P12 QA-P16
QG-P1 QG-P13 QA-P16
QG-P1 QG-P15 QA-P1
QG-P1 QG-P16 Point at infinity QA-L4
QG-P1 QG-P17 QA-P12
QG-P1 QG-P18 QA-Px
QG-P1 QG-P19 QA-Px
QG-P1 QL-P1 QA-P3
QG-P1 QL-P10 QA-P12
QG-P1 QL-P12 QA-P43
QG-P1 QL-P13 QA-P16
QG-P1 All Component Triangles (QA-4Tr1) Desmic
QG-P2 QG-P4 QA-P5
QG-P2 QG-P8 QA-P1.QA-P10 (3:2)
QG-P2 QG-P12 QA-P1
QG-P2 QG-P15 QA-P20
QG-P2 QL-P5 QA-P1
QG-P2 QL-P7 QA-P1
QG-P2 QL-P12 QA-P1
QG-P2 QL-P20 QA-P1
QG-P2 QL-P22 QA-P1
QG-P2 QL-P23 QA-P1
QG-P2 All Component Triangles (QA-4Tr1) Desmic
QG-P3 QL-P15 QA-P43
QG-P4 QG-P8 QA-P1
QG-P4 QG-P12 QA-P5.QA-P16 ^ polar QA-P16 wrt QA-DT-conic(QA-P10,QA-P17)
QG-P4 QG-P15 QA-P1
QG-P4 QL-P12 QA-P10
QG-P5 QG-P10 QA-P1
QG-P5 QL-P1 QA-Px
QG-P5 QL-P2 QA-P24
QG-P7 QG-P9 QA-P1
QG-P7 QL-P2 Midpoint (QA-P1, QA-P33)
QG-P7 QL-P6 QA-Px
QG-P8 QG-P12 QA-Px
QG-P8 QG-P15 QA-P1
QG-P8 QL-P12 QA-P26
QG-P9 QL-P6 QA-P11.QA-P32 (2:1)
QG-P10 QL-P2 QA-P14
QG-P10 QL-P10 QA-P14
QG-P12 QG-P13 QA-P16
QG-P12 QG-P14 QA-Px
QG-P12 QG-P15 Point on QA-Cu2: QA-P1.QA-P17 ^ QA-P16.QA-P20
QG-P12 QG-P17 QA-Px
QG-P12 QL-P5 QA-P1
QG-P12 QL-P7 QA-P1
QG-P12 QL-P12 QA-P1
QG-P12 QL-P13 QA-P16
QG-P12 QL-P20 QA-P1
QG-P12 QL-P22 QA-P1
QG-P12 QL-P23 QA-P1
QG-P12 QL-P26 QA-P8.QA-P23 ^ QA-P2.QA-P7
QG-P13 QL-P13 QA-P16
QG-P13 QL-P17 QA-P3
QG-P14 QG-P15 QA-P5
QG-P15 QL-P12 QA-P1.QA-P10 (3:2)
QG-P15 All Component Triangles (QA-4Tr1) Desmic
QG-P16 QL-P1 QA-P4
QG-P16 All Component Triangles (QA-4Tr1) Desmic
QG-P17 QL-P10 QA-P12
QG-P17 All Component Triangles (QA-4Tr1) Desmic
QG-P18 QG-P19 QA-Px
QG-P18 All Component Triangles (QA-4Tr1) Desmic
QG-P19 All Component Triangles (QA-4Tr1) Desmic
QL-P1 All Component Triangles (QA-4Tr1) Desmic
QL-P2 QL-P3 QA-P15
QL-P2 QL-P10 QA-P14
QL-P2 QL-P29 QA-P15
QL-P3 QL-P29 QA-P15
QL-P5 QL-P7 QA-P1
QL-P5 QL-P12 QA-P1
QL-P5 QL-P20 QA-P1
QL-P5 QL-P22 QA-P1
QL-P5 QL-P23 QA-P1
QL-P7 QL-P12 QA-P1
QL-P7 QL-P20 QA-P1
QL-P7 QL-P22 QA-P1
QL-P7 QL-P23 QA-P1
QL-P12 QL-P20 QA-P1
QL-P12 QL-P22 QA-P1
QL-P12 QL-P23 QA-P1
QL-P20 QL-P22 QA-P1
QL-P20 QL-P23 QA-P1
QL-P22 QL-P23 QA-P1

QA-Px stands for some QA-point that is not registered in EQF.

Points indicated by *) are found by Eckart Schmidt. See [34], QFG#1268.

Apart from the configuration where some Triple Triangles are Desmic with the QA-Component Triangles, there also is a situation where a set of 3 different Triple Triangles form a desmic configuration. Especially the desmic configuration of Triple Triangles QG-P2, QG-P8, QG-P15 is noteworthy as well as the desmic configuration of Triple Triangles QG-P1, QG-P18, QG-P19. Being desmic the triangles have to be mutually perspective. See [34], QFG#2017.




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