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relation: arithmetic cusped orbifold covolumes whose $D=-7$ and $D=-4$ entries have rational multiples among the rows here-- table: HREF{Values_of_the_Clausen_functions_at_rational_multiples_of}[Values of- the Clausen functions at rational multiples of $\pi$]+- table: HREF{Values_of_the_Clausen_functions_at_rational_multiples_of_pi}[Values+ of the Clausen functions at rational multiples of $\pi$] relation: the rows $2,1/3$ and $2,1/2$ are Gieseking's and Catalan's constants, giving closed forms for the figure-eight and Whitehead-link volumes here
comment: It has 1 cusp, an ideal triangulation with 2 tetrahedra, and first homology $\mathbb{Z}/5\oplus\mathbb{Z}$. Its volume is $2\,\mathrm{Cl}_2(\pi/3)$, twice- HREF{Values_of_the_Clausen_functions_at_rational_multiples_of#2,1/3}[Gieseking's+ HREF{Values_of_the_Clausen_functions_at_rational_multiples_of_pi#2,1/3}[Gieseking's constant]. m004:
$\mathbb{Z}$. This is the figure-eight knot complement, HREF{Hyperbolic_volumes_of_the_prime_knots_with_at_most_ten_crossings#4,1}[the $4_1$ row in the table of prime-knot complement volumes]. Its volume is $2\,\mathrm{Cl}_2(\pi/3)$,- twice HREF{Values_of_the_Clausen_functions_at_rational_multiples_of#2,1/3}[Gieseking's+ twice HREF{Values_of_the_Clausen_functions_at_rational_multiples_of_pi#2,1/3}[Gieseking's constant]. m006:
$\mathbb{Z}\oplus\mathbb{Z}$. This is the Whitehead link complement, the link $5^2_1$ of Rolfsen's table. Its volume is $4G=4\,\mathrm{Cl}_2(\pi/2)$, where- $G$ is HREF{Values_of_the_Clausen_functions_at_rational_multiples_of#2,1/2}[Catalan's+ $G$ is HREF{Values_of_the_Clausen_functions_at_rational_multiples_of_pi#2,1/2}[Catalan's constant]. m130:
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