diff --git a/build/pkgs/polymake/checksums.ini b/build/pkgs/polymake/checksums.ini
index 2727d96238b..eba30ebcced 100644
--- a/build/pkgs/polymake/checksums.ini
+++ b/build/pkgs/polymake/checksums.ini
@@ -1,5 +1,5 @@
 tarball=polymake-VERSION-minimal.tar.bz2
-sha1=a3903ef9438388e56a76cb04918c1fe9b2e2b563
-md5=9a451d56cfe8c6138b91558d6d369dbe
-cksum=1195315956
+sha1=e34a9cb83a831b4b058e0803a606f29ff940a4e2
+md5=2118f0cae2f512b994bbc72552966bb9
+cksum=2954910267
 upstream_url=https://polymake.org/lib/exe/fetch.php/download/polymake-VERSION-minimal.tar.bz2
diff --git a/build/pkgs/polymake/dependencies b/build/pkgs/polymake/dependencies
index b3ed8ed4299..c7df48724c2 100644
--- a/build/pkgs/polymake/dependencies
+++ b/build/pkgs/polymake/dependencies
@@ -1,4 +1,4 @@
-$(MP_LIBRARY) bliss cddlib normaliz perl_term_readline_gnu ppl perl_cpan_polymake_prereq libxml2 | ninja_build
+$(MP_LIBRARY) bliss cddlib normaliz perl_term_readline_gnu ppl perl_cpan_polymake_prereq libxml2 lrslib | ninja_build
 
 ----------
 All lines of this file are ignored except the first.
diff --git a/build/pkgs/polymake/package-version.txt b/build/pkgs/polymake/package-version.txt
index 4f8c639658e..86a9588adcd 100644
--- a/build/pkgs/polymake/package-version.txt
+++ b/build/pkgs/polymake/package-version.txt
@@ -1 +1 @@
-4.7
+4.9
diff --git a/build/pkgs/polymake/spkg-install.in b/build/pkgs/polymake/spkg-install.in
index 827409cccd2..36e32de869e 100644
--- a/build/pkgs/polymake/spkg-install.in
+++ b/build/pkgs/polymake/spkg-install.in
@@ -21,6 +21,10 @@ if [ -x $SAGE_LOCAL/bin/lrs1 ]; then
     more_configure_options="$more_configure_options --with-lrs=$SAGE_LOCAL"
 fi
 
+# Put these includes on the front, to avoid shadowing by installed headers
+# from a previous version. (polymake 4.8 puts these includes to the end.)
+export CXXFLAGS="-I$(pwd)/include/core-wrappers -I$(pwd)/include/core $CXXFLAGS"
+
 ./configure --without-java \
             --without-javaview \
             --without-soplex \