Can't a class have static constexpr member instances of itself?

A class is allowed to have a static member of the same type. However, a class is incomplete until the end of its definition, and an object cannot be defined with incomplete type. You can declare an object with incomplete type, and define it later where it is complete (outside the class).

struct Size
{
    const unsigned int width;
    const unsigned int height;

    static const Size big;
    static const Size small;

private:

    Size( ) = default;
};

const Size Size::big = { 480, 240 };
const Size Size::small = { 210, 170 };

see this here: http://coliru.stacked-crooked.com/a/f43395e5d08a3952

This doesn't work for constexpr members, however.

Is there a way to achieve the same result?

By "the same result", do you specifically intend the constexpr-ness of Size::big and Size::small? In that case maybe this would be close enough:

struct Size
{
    const unsigned int width = 0;
    const unsigned int height = 0;

    static constexpr Size big() {
        return Size { 480, 240 };
    }

    static constexpr Size small() {
        return Size { 210, 170 };
    }

private:

    constexpr Size() = default;
    constexpr Size(int w, int h )
    : width(w),height(h){}
};

static_assert(Size::big().width == 480,"");
static_assert(Size::small().height == 170,"");

As a workaround you can use a separate base class which definition is complete when defining the constants in the derived class.

struct size_impl
{
//data members and functions here
    unsigned int width;
    unsigned int height;
};


struct size:  public size_impl
{
//create the constants as instantiations of size_impl
    static constexpr size_impl big{480,240};
    static constexpr size_impl small{210,170};

//provide implicit conversion constructor and assignment operator
    constexpr size(const size_impl& s):size_impl(s){}
    using size_impl::operator=;

//put all other constructors here
};

//test:
constexpr size a = size::big;

You can put the base class in a separate namespace to hide its definition if you want to.

The code compiles with clang and gcc