MathDB

Starting from a pyramid

T_0

whose edges are all of length

2019

, we construct the Figure

T_1

when considering the triangles formed by the midpoints of the edges of each face of

T_0

, building in each of these new pyramid triangles with faces identical to base. Then the bases of these new pyramids are removed. Figure

T_2

is constructed by applying the same process from

T_1

on each triangular face resulting from

T_1

, and so on for

T_3, T_4, ...

Let

D_0= \max \{d(x,y)\}

, where

x

and

y

are vertices of

T_0

and

d(x,y)

is the distance between

x

and

y

. Then we define

D_{n + 1} = \max \{d (x, y) |d (x, y) \notin \{D_0, D_1,...,D_n\}

, where

x, y

are vertices of

T_{n+1}

.
Find the value of

D_n

for all

n

6