Create a right-angled triangular prism in OpenGL

I'm learning OpenGL (specifically, using JOGL) and I'm trying to create a right-angled triangular prism. I learned you can create an equilateral prism with glutWire/SolidCylinder and a a low number of slices (3 for a triangle, obviously).

So I'm wondering if there's some other way to make a prism, or if there's some way to scale an equilateral triangle to turn it into a right triangle?

I additionally found that (at least in JOGL, no idea about elsewhere) glutSolidCylinder doesn't work correctly - the endplates are drawn at a different rotation than the sides, giving you a very strange looking shape.

So I ended up just making a method that creates a unit-right-triangular prism which you can then rotate and scale as necessary. There's likely much better ways to do this, so comments are welcome:

 private void unitTriangularPrism(GL gl, boolean solid){
    // back endcap
    gl.glBegin(solid ? GL.GL_TRIANGLES : GL.GL_LINES);
    gl.glVertex3f(1f, 0f, 0f);
    gl.glVertex3f(0f, 0f, 0f);
    gl.glVertex3f(0f, 1f, 0f);
    gl.glEnd();

    // front endcap
    gl.glBegin(solid ? GL.GL_TRIANGLES : GL.GL_LINES);
    gl.glVertex3f(1f, 0f, 1f);
    gl.glVertex3f(0f, 0f, 1f);
    gl.glVertex3f(0f, 1f, 1f);
    gl.glEnd();

    // bottom
    gl.glBegin(solid ? GL.GL_QUADS : GL.GL_LINES);
    gl.glVertex3f(0f, 0f, 0f);
    gl.glVertex3f(1f, 0f, 0f);
    gl.glVertex3f(1f, 0f, 1f);
    gl.glVertex3f(0f, 0f, 1f);
    gl.glEnd();

    // back
    gl.glBegin(solid ? GL.GL_QUADS : GL.GL_LINES);
    gl.glVertex3f(0f, 0f, 0f);
    gl.glVertex3f(0f, 1f, 0f);
    gl.glVertex3f(0f, 1f, 1f);
    gl.glVertex3f(0f, 0f, 1f);
    gl.glEnd();

    // top
    gl.glBegin(solid ? GL.GL_QUADS : GL.GL_LINES);
    gl.glVertex3f(0f, 1f, 0f);
    gl.glVertex3f(1f, 0f, 0f);
    gl.glVertex3f(1f, 0f, 1f);
    gl.glVertex3f(0f, 1f, 1f);
    gl.glEnd();
}