Take that frown and turn it around A celebration of the many faces of APL
Given a string among those in column 1 or column 2 of the below table, return the string's neighbor to its right. In other words, if given a string in column 1 then return column 2's string on that row, and if given a string in column 2 then return column 3's string on that row.
The codepoints (other than :'s) are listed on the far right.
 column 1   column 2   column 3
 :⊢ → ⍡ → ⊣:   U+22a2  U+2361  U+22a3
 :▷ → ⍢ → ◁:   U+25b7  U+2362  U+25c1
 :⋆ → ⍣ → ⋆:   U+22c6  U+2363  U+22c6
 :∘ → ⍤ → ∘:   U+2218  U+2364  U+2218
 :○ → ⍥ → ○:   U+25cb  U+2365  U+25cb
 :≀ → ⍨ → ≀:   U+2240  U+2368  U+2240
 :∧ → ⍩ → ∨:   U+2227  U+2369  U+2228
Anecdote: Most of these symbols are valid or proposed in some APL dialect (they are all links).
Per request, just the symbols:
:⊢ ⍡ ⊣:
:▷ ⍢ ◁:
:⋆ ⍣ ⋆:
:∘ ⍤ ∘:
:○ ⍥ ○:
:≀ ⍨ ≀:
:∧ ⍩ ∨:
JavaScript (ES6), 108 107 bytes

s=&gt;(S="⊢▷⋆∘○≀∧⍡⍢⍣⍤⍥⍨⍩⊣◁⋆∘○≀∨")[S.search(s[1]||s)+7]+(s[1]?'':':')


Demo



let f =

s=&gt;(S="⊢▷⋆∘○≀∧⍡⍢⍣⍤⍥⍨⍩⊣◁⋆∘○≀∨")[S.search(s[1]||s)+7]+(s[1]?'':':')

;[
  ":⊢", ":▷", ":⋆", ":∘", ":○", ":≀", ":∧",
  "⍡", "⍢", "⍣", "⍤", "⍥", "⍨", "⍩"
]
.forEach(s =&gt; console.log(s + ' → ' + f(s)))