MathDB

ABCD

is a regular tetrahedron with side length 1. Points

X,

Y,

and

Z,

distinct from

A,

B,

and

C,

respectively, are drawn such that

BCDX,

ACDY,

and

ABDZ

are also regular tetrahedra. If the volume of the polyhedron with faces

ABC,

XYZ,

BXC,

XCY,

CYA,

YAZ,

AZB,

and

ZBX

can be written as

\frac{a\sqrt{b}}{c}

for positive integers

a,b,c

with

\gcd(a,c) = 1

and

b

squarefree, find

a+b+c.

Proposed by Jason Wang

Problem Statement