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9
2015 Geometry #9
2015 Geometry #9
Source:
July 1, 2022
2015
Geometry Test
Problem Statement
Regular tetrahedron
A
B
C
D
ABCD
A
BC
D
has center
O
O
O
and side length
1
1
1
. Points
A
′
A'
A
′
,
B
′
B'
B
′
,
C
′
C'
C
′
, and
D
′
D'
D
′
are defined by reflecting
A
A
A
,
B
B
B
,
C
C
C
, and
D
D
D
about
O
O
O
. Compute the volume of the polyhedron with vertices
A
B
C
D
A
′
B
′
C
′
D
′
ABCDA'B'C'D'
A
BC
D
A
′
B
′
C
′
D
′
.
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