I have a 32-bit installer which needs 32-bit libXext.so.6 but my CentOS 6.1 x86_64 installation does not have that. This is the output when I run the installer...
# sh /home/username/iscape.04.21-p004/bin/iscape.sh
Initializing InstallScape using JVM at /home/username/iscape.04.21-p004/runtime/LNX86/bin/java. This might take some time...
Exception in thread "main" java.lang.UnsatisfiedLinkError: /home/username/iscape.04.21-p004/runtime/LNX86/lib/i386/xawt/libmawt.so: libXext.so.6: cannot open shared object file: No such file or directory
at java.lang.ClassLoader$NativeLibrary.load(Native Method)
at java.lang.ClassLoader.loadLibrary0(Unknown Source)
at java.lang.ClassLoader.loadLibrary(Unknown Source)
at java.lang.Runtime.load0(Unknown Source)
at java.lang.System.load(Unknown Source)
at java.lang.ClassLoader$NativeLibrary.load(Native Method)
at java.lang.ClassLoader.loadLibrary0(Unknown Source)
at java.lang.ClassLoader.loadLibrary(Unknown Source)
at java.lang.Runtime.loadLibrary0(Unknown Source)
at java.lang.System.loadLibrary(Unknown Source)
at sun.security.action.LoadLibraryAction.run(Unknown Source)
at java.security.AccessController.doPrivileged(Native Method)
at java.awt.Toolkit.loadLibraries(Unknown Source)
at java.awt.Toolkit.<clinit>(Unknown Source)
at com.khanpur.installer.gui.InstallerUI.main(InstallerUI.java:107)

When I try to locate libXext.so.6 file I get this
# locate libXext.so.6
/usr/lib64/libXext.so.6
/usr/lib64/libXext.so.6.4.0

and when I try to install the 32-bit rpms I get this
# rpm -Uhv libXext-1.3.1-2.el6.i686.rpm
warning: libXext-1.3.1-2.el6.i686.rpm: Header V3 RSA/SHA1 Signature, key ID c105b9de: NOKEY
error: Failed dependencies:
libX11.so.6 is needed by libXext-1.3.1-2.el6.i686
# rpm -Uhv libX11-1.5.0-4.el6.i686.rpm
warning: libX11-1.5.0-4.el6.i686.rpm: Header V3 RSA/SHA1 Signature, key ID c105b9de: NOKEY
error: Failed dependencies:
libX11-common = 1.5.0-4.el6 is needed by libX11-1.5.0-4.el6.i686
libxcb.so.1 is needed by libX11-1.5.0-4.el6.i686
# rpm -Uhv libX11-common-1.5.0-4.el6.noarch.rpm
warning: libX11-common-1.5.0-4.el6.noarch.rpm: Header V3 RSA/SHA1 Signature, key ID c105b9de: NOKEY
error: Failed dependencies:
libX11-common = 1.3-2.el6 is needed by (installed) libX11-1.3-2.el6.x86_64

With this error how can I install 32-bit package?
When I try to install using yum
# yum install libXext-1.3.1-2.el6.i686.rpm
Loaded plugins: product-id, refresh-packagekit, subscription-manager
Updating Red Hat repositories.
Setting up Install Process
No package libXext-1.3.1-2.el6.i686.rpm available.
Error: Nothing to do

I have already added EPEL and RPMForge Repository.

Let yum do the heavy lifting.

cooltoad, The above answer from sag47 is all you need. I just want to also explain what went wrong for you.

An important general rule is to put .i686 after the package name when you want yum to install the 32-bit version.

That tells you that you have the 64 bit version. You probably understood that.

Don't download and install rpm's that way unless you can't get them with yum.

The long chain of manual dependencies is only ONE of multiple reasons why it is better to use yum.

You aren't supposed to type the .rpm part of the name when using yum install. Usually you are not supposed to type the "-1.3.1-2.el6" part either. Usually you should let yum get the current (for your system) version. But you do need the ".i686" part if you don't want the default (x86_64).

Sometimes you need a specific other version, but that can get complicated. Don't ask for a specific version unless you really need it.

Good. But that package is in base.

Couldn't install using yum

# yum search libXext | grep '^libXext'
libXext.x86_64 : X.Org X11 libXext runtime library
libXext-devel.x86_64 : X.Org X11 libXext development package

# yum install libXext.i686
Loaded plugins: product-id, refresh-packagekit, subscription-manager
Updating Red Hat repositories.
Setting up Install Process
No package libXext.i686 available.
Error: Nothing to do

That is a surprising result and you are getting beyond my yum knowledge. But I think the following might yield an explanation:

the repos for centos 6.1 were moved to the archive ( the VAULT) 2 years back
this is the place holder for the 6.1 mirrors
there might be a few mirrors that still have the base repo ??? maybe ???
but all the code is 2 years out of date

CentOS 6.5 is the current

please UPGRADE

6.1 is unsupported and so is 6.2,6.3,and 6.4

libXext would be in the base repo for 6.1 and that is NOT at the location used in the cent.repo
it was MOVED 2 years ago

to see what repos are installed and used
and your version of cent