diff --git a/docs/src/reference/details.yml b/docs/src/reference/details.yml
index 5d740336c..1926fb774 100644
--- a/docs/src/reference/details.yml
+++ b/docs/src/reference/details.yml
@@ -31,7 +31,7 @@ math: |
 
   ```example
   $ A = pi r^2 $
-  $ "area" = pi dot.op "radius"^2 $
+  $ "area" = pi dot "radius"^2 $
   $ cal(A) :=
       { x in RR | x "is natural" } $
   #let x = 5
@@ -39,7 +39,7 @@ math: |
   ```
 
   Math mode makes a wide selection of [symbols]($category/symbols/sym) like
-  `pi`, `dot.op`, or `RR` available. Many mathematical symbols are available in
+  `pi`, `dot`, or `RR` available. Many mathematical symbols are available in
   different variants. You can select between different variants by applying
   [modifiers]($type/symbol) to the symbol. Typst further recognizes a number of
   shorthand sequences like `=>` that approximate a symbol. When such a shorthand
diff --git a/library/src/math/matrix.rs b/library/src/math/matrix.rs
index f2a9fe97e..368cd5c48 100644
--- a/library/src/math/matrix.rs
+++ b/library/src/math/matrix.rs
@@ -10,7 +10,7 @@ const VERTICAL_PADDING: Ratio = Ratio::new(0.1);
 ///
 /// ## Example
 /// ```example
-/// $ vec(a, b, c) dot.op vec(1, 2, 3)
+/// $ vec(a, b, c) dot vec(1, 2, 3)
 ///     = a + 2b + 3c $
 /// ```
 ///
@@ -135,7 +135,7 @@ impl LayoutMath for MatElem {
 /// ## Example
 /// ```example
 /// $ f(x, y) := cases(
-///   1 "if" (x dot.op y)/2 <= 0,
+///   1 "if" (x dot y)/2 <= 0,
 ///   2 "if" x "is even",
 ///   3 "if" x in NN,
 ///   4 "else",
diff --git a/library/src/symbols/sym.rs b/library/src/symbols/sym.rs
index e48452ebe..421efe856 100644
--- a/library/src/symbols/sym.rs
+++ b/library/src/symbols/sym.rs
@@ -64,12 +64,12 @@ pub(crate) const SYM: &[(&str, Symbol)] = symbols! {
     // Punctuation.
     amp: ['&', inv: '⅋'],
     ast: [
-        '*',
+        basic: '*',
+        op: '∗',
         low: '⁎',
         double: '⁑',
         triple: '⁂',
         small: '﹡',
-        op: '∗',
         circle: '⊛',
         sq: '⧆',
     ],
@@ -89,8 +89,8 @@ pub(crate) const SYM: &[(&str, Symbol)] = symbols! {
         wave.double: '〰',
     ],
     dot: [
-        '.',
         op: '⋅',
+        basic: '.',
         c: '·',
         circle: '⊙',
         circle.big: '⨀',
@@ -111,10 +111,10 @@ pub(crate) const SYM: &[(&str, Symbol)] = symbols! {
     section: '§',
     semi: [';', rev: '⁏'],
     slash: ['/', double: '⫽', triple: '⫻'],
-    dots: [h: '…', h.c: '⋯', v: '⋮', down: '⋱', up: '⋰'],
+    dots: [h.c: '⋯', h: '…', v: '⋮', down: '⋱', up: '⋰'],
     tilde: [
-        '~',
         op: '∼',
+        basic: '~',
         eq: '≃',
         eq.not: '≄',
         eq.rev: '⋍',
diff --git a/tests/ref/math/syntax.png b/tests/ref/math/syntax.png
index f223ba5ae..3779f9a8f 100644
Binary files a/tests/ref/math/syntax.png and b/tests/ref/math/syntax.png differ
diff --git a/tests/typ/math/cases.typ b/tests/typ/math/cases.typ
index 83a5ab66f..d591ae50e 100644
--- a/tests/typ/math/cases.typ
+++ b/tests/typ/math/cases.typ
@@ -2,7 +2,7 @@
 
 ---
 $ f(x, y) := cases(
-  1 quad &"if" (x dot.op y)/2 <= 0,
+  1 quad &"if" (x dot y)/2 <= 0,
   2 &"if" x divides 2,
   3 &"if" x in NN,
   4 &"else",
diff --git a/tests/typ/math/matrix.typ b/tests/typ/math/matrix.typ
index e57e102e4..c1fba6277 100644
--- a/tests/typ/math/matrix.typ
+++ b/tests/typ/math/matrix.typ
@@ -3,12 +3,12 @@
 ---
 // Test semicolon syntax.
 #set align(center)
-$mat() dot.op
- mat(;) dot.op
- mat(1, 2) dot.op
+$mat() dot
+ mat(;) dot
+ mat(1, 2) dot
  mat(1, 2;) \
- mat(1; 2) dot.op
- mat(1, 2; 3, 4) dot.op
+ mat(1; 2) dot
+ mat(1, 2; 3, 4) dot
  mat(1 + &2, 1/2; &3, 4)$
 
 ---
diff --git a/tests/typ/math/multiline.typ b/tests/typ/math/multiline.typ
index 4f42ea63a..b1f438006 100644
--- a/tests/typ/math/multiline.typ
+++ b/tests/typ/math/multiline.typ
@@ -4,13 +4,13 @@
 // Test basic alignment.
 $ x &= x + y \
     &= x + 2z \
-    &= sum x dot.op 2z $
+    &= sum x dot 2z $
 
 ---
 // Test text before first alignment point.
 $ x + 1 &= a^2 + b^2 \
       y &= a + b^2 \
-      z &= alpha dot.op beta $
+      z &= alpha dot beta $
 
 ---
 // Test space between inner alignment points.
diff --git a/tests/typ/math/syntax.typ b/tests/typ/math/syntax.typ
index 26d3e4449..17633357b 100644
--- a/tests/typ/math/syntax.typ
+++ b/tests/typ/math/syntax.typ
@@ -12,6 +12,10 @@ $ underline(f' : NN -> RR) \
     2 * 3 &"if" n != 5,
     1 - 0 thick &...,
   ) $
+  
+---
+// Test common symbols.
+$ dot \ dots \ ast \ tilde \ star $
 
 ---
 // Error: 1:3 expected dollar sign