A hypercube is a shape constructed by repeatedly taking the prism of a point (each prism being of identical length). Each hypercube has three hypercubes of the lower dimension surrounding each peak (e.g. a cube has three squares around each vertex, a tesseract has three cubes around each edge, etc.)
{ 3 n − 1 } {\displaystyle \{3^{n-1}\}}
) ( {\displaystyle )(} ∅ {\displaystyle \emptyset}
( ) {\displaystyle ()} B 0 {\displaystyle \mathbb{B}^0}
{ } {\displaystyle \{\}} B 1 {\displaystyle \mathbb{B}^1}
{ 3 } {\displaystyle \{3\}}
{ 3 2 } {\displaystyle \{3^2\}}
{ 3 3 } {\displaystyle \{3^3\}}
{ 3 4 } {\displaystyle \{3^4\}}
{ 3 5 } {\displaystyle \{3^5\}}
{ 3 6 } {\displaystyle \{3^6\}}
{ 3 7 } {\displaystyle \{3^7\}}
{ 3 8 } {\displaystyle \{3^8\}}
{ 3 9 } {\displaystyle \{3^9\}}
{ 3 10 } {\displaystyle \{3^{10}\}}
{ 3 11 } {\displaystyle \{3^{11}\}}
{ 3 12 } {\displaystyle \{3^{12}\}}
{ 3 13 } {\displaystyle \{3^{13}\}}
{ 3 14 } {\displaystyle \{3^{14}\}}
{ 3 15 } {\displaystyle \{3^{15}\}}
{ 3 16 } {\displaystyle \{3^{16}\}}
{ 3 n − 2 , 4 } {\displaystyle \{3^{n-2},4\}}
{ 4 } {\displaystyle \{4\}}
{ 3 , 4 } {\displaystyle \{3, 4\}}
{ 3 2 , 4 } {\displaystyle \{3^2, 4\}}
{ 3 3 , 4 } {\displaystyle \{3^3, 4\}}
{ 3 4 , 4 } {\displaystyle \{3^4, 4\}}
{ 3 5 , 4 } {\displaystyle \{3^5, 4\}}
{ 3 6 , 4 } {\displaystyle \{3^6, 4\}}
{ 3 7 , 4 } {\displaystyle \{3^7, 4\}}
{ 3 8 , 4 } {\displaystyle \{3^8, 4\}}
{ 3 9 , 4 } {\displaystyle \{3^9, 4\}}
{ 3 10 , 4 } {\displaystyle \{3^{10}, 4\}}
{ 3 11 , 4 } {\displaystyle \{3^{11}, 4\}}
{ 3 12 , 4 } {\displaystyle \{3^{12}, 4\}}
{ 3 13 , 4 } {\displaystyle \{3^{13}, 4\}}
{ 3 14 , 4 } {\displaystyle \{3^{14}, 4\}}
{ 3 15 , 4 } {\displaystyle \{3^{15},4\}}
{ 3 n − 2 , 5 } {\displaystyle \{3^{n-2}, 5\}}
{ 5 } {\displaystyle \{5\}}
{ 3 , 5 } {\displaystyle \{3, 5\}}
{ 3 2 , 5 } {\displaystyle \{3^2, 5\}}
{ 3 3 , 5 } {\displaystyle \{3^3, 5\}}
{ 3 4 , 5 } {\displaystyle \{3^4, 5\}}
{ 4 , 3 n − 2 } {\displaystyle \{4, 3^{n-2}\}}
{ 4 , 3 } {\displaystyle \{4,3\}}
{ 4 , 3 2 } {\displaystyle \{4, 3^2\}}
{ 4 , 3 3 } {\displaystyle \{4, 3^3\}}
{ 4 , 3 4 } {\displaystyle \{4, 3^4\}}
{ 4 , 3 5 } {\displaystyle \{4, 3^5\}}
{ 4 , 3 6 } {\displaystyle \{4, 3^6\}}
{ 4 , 3 7 } {\displaystyle \{4, 3^7\}}
{ 4 , 3 8 } {\displaystyle \{4, 3^8\}}
{ 4 , 3 9 } {\displaystyle \{4, 3^9\}}
{ 4 , 3 10 } {\displaystyle \{4, 3^{10}\}}
{ 4 , 3 11 } {\displaystyle \{4, 3^{11}\}}
{ 4 , 3 12 } {\displaystyle \{4, 3^{12}\}}
{ 4 , 3 13 } {\displaystyle \{4, 3^{13}\}}
{ 4 , 3 14 } {\displaystyle \{4, 3^{14}\}}
{ 4 , 3 15 } {\displaystyle \{4,3^{15}\}}
{ 5 , 3 n − 2 } {\displaystyle \{5, 3^{n-2}\}}
{ 5 , 3 } {\displaystyle \{5, 3\}}
{ 5 , 3 2 } {\displaystyle \{5, 3^2\}}
{ 5 , 3 3 } {\displaystyle \{5, 3^3\}}
{ 5 , 3 4 } {\displaystyle \{5, 3^4\}}
B n {\displaystyle \mathbb B^n}
B 2 {\displaystyle \mathbb B^2}
B 3 {\displaystyle \mathbb B^3}
B 4 {\displaystyle \mathbb B^4}
B 5 {\displaystyle \mathbb B^5}
B 6 {\displaystyle \mathbb B^6}
B 7 {\displaystyle \mathbb B^7}
B 8 {\displaystyle \mathbb B^8}
B 9 {\displaystyle \mathbb B^9}
B 10 {\displaystyle \mathbb B^{10}}
B 11 {\displaystyle \mathbb B^{11}}
B 12 {\displaystyle \mathbb B^{12}}
B 13 {\displaystyle \mathbb B^{13}}
B 14 {\displaystyle \mathbb B^{14}}
B 15 {\displaystyle \mathbb B^{15}}
B 16 {\displaystyle \mathbb B^{16}}
B 17 {\displaystyle \mathbb {B} ^{17}}
B ℵ 0 {\displaystyle \mathbb B^{\aleph_0}}
