MathDB

Let

ABCD

be a regular triangular pyramid with base

ABC

(this means that

ABC

is a regular triangle, and edges

AD

BD

and

CD

are equal) and plane angles at the opposite vertex equal to

a

. A plane parallel to

ABC

intersects

AD

BD

and

CD

, respectively, at points

A_1

B_1

and

C_1

. The surface of the polyhedron

ABCA_1B_1C_1

is cut along five edges:

A_1B_1

B_1C_1

C_1C

CA

and

AB

, after which this surface is turned onto a plane. At what values of

a

will the resulting scan necessarily cover itself?

Problem Statement