Tetrahedron

Initial vertex: v1=[001]

Transforms for vertex generation:

T~i∈{[100010001],[−12−123−2312356−13223−132−13],[−12−1230123−120001]}

T3V3=[01322−13]=V2
T2V2=[23−132−13]=V3
T2V1=[−23−132−13]=V4
T2T2=[−1212323−12356−132−23−132−13]=T4
T3T2=[0−1323−13−23−13223−132−13]=T5
T3T4=[12−1230−123−161322−23−132−13]=T6
T2T5=[−121230−123−120001]=T7
T3T5=[121230123−16132223−132−13]=T8
T3T6=[013−2313−23−132−23−132−13]=T9
T2T7=[12−123−23−123−16−13201322−13]=T10
T2T8=[−100013132201322−13]=T11
T2T9=[1212323123−16−13201322−13]=T12
Vertexes as column vectors:

V=[0023−2301322−132−1321−13−13−13]

Vertex inner products:

VTV=[00101322−1323−132−13−23−132−13][0023−2301322−132−1321−13−13−13]=[1−13−13−13−131−13−13−13−131−13−13−13−131]

Table of Ti⋅vj=vk:
V1 V2 V3 V4
T1 V1 V2 V3 V4
T2 V4 V2 V1 V3
T3 V1 V4 V2 V3
T4 V3 V2 V4 V1
T5 V3 V4 V1 V2
T6 V2 V4 V3 V1
T7 V1 V3 V4 V2
T8 V2 V3 V1 V4
T9 V4 V3 V2 V1
T10 V4 V1 V3 V2
T11 V2 V1 V4 V3
T12 V3 V1 V2 V4


Table of Ti⋅Tj=Tk:
T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12
T1 T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12
T2 T2 T4 T9 T1 T7 T8 T10 T11 T12 T5 T6 T3
T3 T3 T5 T7 T6 T8 T9 T1 T2 T4 T12 T10 T11
T4 T4 T1 T12 T2 T10 T11 T5 T6 T3 T7 T8 T9
T5 T5 T6 T4 T3 T1 T2 T12 T10 T11 T8 T9 T7
T6 T6 T3 T11 T5 T12 T10 T8 T9 T7 T1 T2 T4
T7 T7 T8 T1 T9 T2 T4 T3 T5 T6 T11 T12 T10
T8 T8 T9 T6 T7 T3 T5 T11 T12 T10 T2 T4 T1
T9 T9 T7 T10 T8 T11 T12 T2 T4 T1 T3 T5 T6
T10 T10 T11 T2 T12 T4 T1 T9 T7 T8 T6 T3 T5
T11 T11 T12 T8 T10 T9 T7 T6 T3 T5 T4 T1 T2
T12 T12 T10 T5 T11 T6 T3 T4 T1 T2 T9 T7 T8